! ~, how to use these symbols in writing novels? Please give an example

! ~, how to use these symbols in writing novels? Please give an example

? The question mark...is in the question sentence

! Expressing surprise...

~ Well... if you want to submit a manuscript, it is best not to use it... Editors are very annoying...

Period... is used when finishing a sentence.

Comma... is used to break the sentence... to indicate a general pause within the sentence.

How to use emphasis marks? Please give an example and explain.

The emphasis mark (·) is a symbol used to attract the reader's attention. When used, it is dotted below the text; when used in vertical format, it is marked on the right side of the word. "Words, words, and sentences that require readers to pay special attention are marked with emphasis."

Usage

In Hong Kong, emphasis is usually only used in textbooks or teaching materials. The usage method is the same as that in mainland China.

The form of emphasis mark is a small dot. The midpoint of horizontal text is below the word, and the midpoint of straight text is on the right side of the word.

Example

Emphasis marks (·) mark the words, words, and sentences that require readers to pay special attention. For example:

Careers are created by hard work, not by boasting.

◥▇▆▅︻How to avoid copying this symbol? Please give examples of other strange symbols! Thanks!

There is one in Sogou Input Method. The hotkey Ctrl Shift z turns on "Special Symbols". Select it there.

What are the common uses of derivatives? Please give an example!

Application

1. Monotonicity of a function

(1) Use the sign of the derivative to judge the increase or decrease of the function. This is the geometric significance of the derivative when studying the law of curve change. An application that fully embodies the idea of ??combining numbers and shapes. Generally, in a certain interval (a, b), if f'(x)gt; 0, then the function y=f(x) increases monotonically in this interval; if f'(x)lt; 0, Then the function y=f(x) decreases monotonically in this interval. If f'(x)=0 always exists in a certain interval, then f(x) is a constant function. Note: In a certain interval, f'(x)gt; 0 is a sufficient condition for f(x) to be an increasing function in this interval, not a necessary condition. For example, f(x)=x3 is an increasing function in R. function, but f'(x)=0 when x=0. In other words, if it is known that f(x) is an increasing function, you must write f'(x)≥0 when solving the problem. (2) Steps to find the monotonic interval of a function (1. Definition of the most basic method 2. Monotonicity of compound functions) ① Determine the domain of f(x) ② Find the derivative ③ Solve the corresponding range of x from (or). When f'(x)gt;0, f(x) is an increasing function on the corresponding interval; when f'(x)lt;0, f(x) is a decreasing function on the corresponding interval.

2. Extreme value of a function

(1) Judgment of the extreme value of a function ① If the signs on both sides are the same, it is not the extreme point of f(x) ② If the signs on the nearby left and right sides are different, Then, is it a maximum value or a minimum value.

3. Steps to find the extreme value of a function

① Determine the domain of the function ② Find the derivative ③ Find all stationary points and points where derivatives do not exist in the domain, that is, find all the real roots of the equation and ④ Check the signs around the stationary point. If the left is positive and the right is negative, then f(x) takes the maximum value at this root; if the left is negative and the right is positive, then f(x) takes the minimum value at this root.

4. The maximum value of the function

(1) If the maximum value (or minimum value) of f(x) on [a, b] is obtained at a point in (a, b), obviously this The maximum value (or minimum value) is also a maximum value (or minimum value), which is the maximum (or minimum) of all the maximum values ??(or minimum values) of f(x) in (a, b) ), but the maximum value may also be obtained at the endpoint a or b of [a, b]. The extreme value and the maximum value are two different concepts. (2) Steps to find the maximum and minimum values ??of f(x) on [a, b] ① Find the extreme value of f(x) in (a, b) ② Compare each extreme value of f(x) with Compare f(a) and f(b), the largest one is the maximum value, and the smallest one is the minimum value.

5. Optimization problems in life

In life, we often encounter problems such as maximizing profits, saving the most materials, and maximizing efficiency. These problems are called optimization problems, and optimization problems are also called optimal value problems. Solving these problems has very practical significance. These problems can usually be transformed into function problems in mathematics, and then into the problem of finding the maximum (minimum) value of the function.

Definition

Suppose the function y=f(x) is defined in a certain neighborhood N(x0, δ) of point x0. When the independent variable x has Increment △x (assuming x0 △x∈N(x0, δ)), the corresponding increment of the function y=f(x) is △y=f(x0 △x)-f(x0). If when △x →0, the limit lim of the ratio of the increment △y of the function to the increment △x of the independent variable △y/△x=lim [f(x0 △x)-f(x0)]/△x exists, then This limit value is called the derivative or rate of change of f(x) at x0. It can usually be written as f'(x0) or f'(x)|x=x0.

Differentiability of the function Properties and derivative functions

Generally speaking, assuming that the unary function y=f(x) is defined in a certain neighborhood N(x0, δ) of point x0, when the independent variable takes the increment When Δx=x-x0, the corresponding increment of the function is △y=f(x0 △x)-f(x0). If the ratio of the function increment △y to the independent variable increment △x is △x→0 The limit exists and is finite, it is said that the function f(x) is differentiable at point x0, and this limit is called the derivative or rate of change of f at point x0.

"Point to form a line": If the function f is differentiable at every point in the interval I, a new function with I as its domain will be obtained, denoted as f(x)' or y', which is called the function of f The derivative function, referred to as the derivative.

The geometric meaning of the derivative

The geometric meaning of the derivative f' (x0) of the function y=f (x) at the x0 point: represents the function The tangent slope of the formula curve at the point P0 [the geometric meaning of the x derivative

0, f (x0)] (the geometric meaning of the derivative is the tangent slope of the function curve at this point).

Application of derivatives in science

Derivatives are closely related to physics, geometry, and algebra. In geometry, tangent lines can be found; in algebra, instantaneous rates of change can be found; in physics, velocity can be found. Acceleration. Derivative, also known as algebra and derivative (a concept in differential calculus), is a mathematical concept abstracted from the speed change problem and the tangent problem of the curve (the direction of the vector speed). It is also called the rate of change. For example, a car rotates at 10 It travels 600 kilometers per hour, and its average speed is 60 kilometers/hour. But in the actual driving process, the speed changes, and it is not always 60 kilometers/hour. In order to better reflect the driving process of the car The time interval can be shortened by changing the speed in -f(t0)]/[t1-t0] When t1 and t0 are very close, the speed of the car will not change much, and the average speed can better reflect the movement of the car from t0 to t1. Changes. Naturally, the limit lim[f(t1)-f(t0)]/[t1-t0] when t1→t0 is taken as the instantaneous speed of the car at time t0, which is what is usually called speed. This is actually The above is the process of analogy from average speed to instantaneous speed (for example, the "speed limit" when we drive refers to instantaneous speed)

Edit this paragraph Derivatives are an important concept in calculus

Another definition of derivative: when x=x0, f'(x0) is a definite number. In this way, when x changes, f'(x) is a function of x. We call it the derivative function of f(x) (referred to as the derivative).

y= The derivative of f(x) is sometimes also recorded as y', that is (as shown on the right): Some important concepts in physics, geometry, economics and other disciplines can be expressed by derivatives. For example, the derivative can represent the instantaneous velocity and acceleration of a moving object (take uniform linear acceleration as an example. The first derivative of displacement with respect to time is the instantaneous velocity and the second derivative is acceleration). It can represent the slope of the curve at a point (the direction of the vector velocity). , can also represent marginal and elasticity in economics. The definition of classical derivative mentioned above can be considered as reflecting the function change of regional Euclidean space. In order to study the changes in the cross-section of vector bundles on more general manifolds (such as tangent vector fields), the concept of derivatives is generalized to the so-called "connection". With liaison, one can study a wide range of geometric problems, which is one of the most important fundamental concepts in differential geometry and physics. Note: 1.f'(x)lt;0 is a sufficient and unnecessary condition for f(x) to be a subtraction function, but it is not a necessary and sufficient condition. 2. The point where the derivative is zero is not necessarily the extreme point. When the function is a constant value function, there is no increase or decrease, that is, there is no extreme point. But the derivative is zero. (The point with zero derivative is called a stationary point. If the signs of the derivatives on both sides of the stationary point are opposite, the point is an extreme point, otherwise it is a general stationary point, such as f'(0) in y=x^3 =0, the sign of the left and right derivatives of x=0 is positive, and this point is a general stationary point)

Edit this paragraph to find the derivative method

(1) Use the definition to find the function. Steps for the derivative of y=f(x) at x0: ① Find the increment of the function Δy=f(x0 Δx)-f(x0) ② Find the average rate of change

③ Take the limit and get the derivative .

(2) Derivative formulas of several common functions: ① C'=0 (C is a constant function) ② (x^n)'= nx^(n-1) (n∈Q*); memorize 1/ Derivative of (sinx)^2=(cscx)^2=1 (cotx)^2 (secx)'=tanx·secx (cscx)'=-cotx·cscx (arcsinx)'=1/(1-x^2)^ 1/2 (arosx)'=-1/(1-x^2)^1/2 (arctanx)'=1/(1 x^2) (arotx)'=-1/(1 x^2) ( arcsecx)'=1/(|x|(x^2-1)^1/2) (arscx)'=-1/(|x|(x^2-1)^1/2) ④(sinhx) '=coshx (coshx)'=sinhx (tanhx)'=1/(coshx)^2=(sechx)^2 (coth)'=-1/(sinhx)^2=-(cschx)^2 (sechx) '=-tanhx·sechx (cschx)'=-cothx·cschx (arsinhx)'=1/(x^2 1)^1/2 (arcoshx)'=1/(x^2-1)^1/2 (artanhx)'=1/(x^2-1) (|x|lt;1) (arcothx)'=1/(x^2-1) (|x|gt;1) (arsechx)'=1 /(x(1-x^2)^1/2) (arcschx)'=1/(x(1 x^2)^1/2) ⑤ (e^x)' = e^x (a^x )' = (a^x)lna (ln is the natural logarithm) (Inx)' = 1/x (ln is the natural logarithm) (logax)' =x^(-1) /lna(agt; 0 and a Not equal to 1) (x^1/2)'=[2(x^1/2)]^(-1) (1/x)'=-x^(-2) Just to add. The above formula cannot be substituted for constants, but can only be substituted for functions. People who are new to derivatives often ignore this point, causing ambiguity, so please pay more attention. Regarding trigonometric derivation, "positive plus co-negative" (triangle includes trigonometric functions, and also includes inverse trigonometric functions, namely sine, tangent and secant.) (3) The four operating rules of derivatives (sum, difference, product, quotient ): ①(u±v)'=u'±v' ②(uv)'=u'v uv' ③(u/v)'=(u'v-uv')/ v^2 4. Derivative of a composite function: The derivative of a composite function with respect to the independent variables is equal to the derivative of the known function with respect to the intermediate variables, multiplied by the derivative of the intermediate variables with respect to the independent variables - called the chain rule. 5. Derivative method under the integral sign d(∫f(x, t)dt φ(x), ψ(x))/dx=f(x, ψ(x))ψ'(x)-f(x, φ (x))φ'(x) ∫[f 'x(x,t)dt φ(x),ψ(x)] Derivatives are an important pillar of calculus.

Newton and Leibniz made outstanding contributions to this!

Edit the derivative formulas and proofs of this paragraph

Here we will list the derivatives of five basic elementary functions and their derivation processes (elementary functions can be calculated by them): Basic derivative formula

1. Constant function (i.e. constant) y=c (c is a constant) y'=0 2. Power function y=x^n, y'=nx^(n-1)( n∈Q*) Memorize the derivative of 1/X 3. Exponential function (1) y=a^x, y'=a^xlna; (2) Memorize y=e^x y'=e^x is the only function whose derivative is itself 4. Logarithmic function (1) y=logaX, y'=1/xlna (agt; 0 and a is not equal to 1, xgt; 0); memorize y=lnx, y'=1/x 5. Sine function y=(sinx)y'=cosx 6. Cosine function y=(cosx) y'=-sinx 7. Tangent function y=(tanx) y'=1/(cosx)^2 8. Cotangent function y=(cotx) y'=-1/(sinx)^2 9. Arcsine function y=(arcsinx) y'=1/√1-x^2 10. Inverse cosine function y=(arosx) y'=-1/√1-x^2 11. Arctangent function y=(arctanx) y'=1/(1 x^2) 12. Inverse cotangent function y=(arotx) y'=-1/(1 x^2) In order to facilitate memory, someone compiled the following formula: Always zero, the power is reduced to the first degree, and the reciprocal (when e is the base, directly reciprocal , multiplied by lna when a is the base), means unchanged (in particular, the exponential function of the natural logarithm is completely unchanged, and the general exponential function must be multiplied by lna); positive changes to co, co changes to positive, and the cutting square ( The tangent function is the square of the corresponding cut function (the reciprocal of the tangent function), the cut times the tangent, and the inverse fraction. There are several common formulas that need to be used in the derivation process: 1.y=f[g( x)], y'=f'[g(x)]·g'(x)'f'[g(x)], g(x) is regarded as the entire variable, and g'(x), x is regarded as Make a variable' 2. y=u/v, y'=(u'v-uv')/v^2 3. The relationship between the derivatives of the original function and the inverse function (the inverse trigonometric function is deduced from the derivative of the trigonometric function): the inverse function of y=f(x) is x=g(y), then y'=1/x' Proof: 1. Obviously, y=c is a straight line parallel to the x-axis, so the tangent lines everywhere are parallel to x, so the slope is 0. The same is true with the definition of derivatives: y=c, Δy=c-c=0, limΔx→0Δy/Δx=0. 2. The derivation of this is not proved for the time being, because if the derivation is based on the definition of the derivative, it cannot be extended to the general case where n is any real number, and it can only be proved that it is an integer Q. Mainly apply the definition of derivative and the N-order variance formula. After obtaining the two results y=e^x y'=e^x and y=lnx y'=1/x, we can use the derivation of the composite function to prove it. 3． y=a^x, Δy=a^(x Δx)-a^x=a^x(a^Δx-1) Δy/Δx=a^x(a^Δx-1)/Δx If we directly let Δx→ 0, the derivative function cannot be exported, and an auxiliary function β=a^Δx-1 must be set for calculation by substitution. It can be known from the assumed auxiliary function: Δx=loga(1 β). So (a^Δx-1)/Δx=β/loga(1 β)=1/loga(1 β)^1/β Obviously, when Δx→0, β also tends to 0. And limβ→0(1 β)^1/β=e, so limβ→01/loga(1 β)^1/β=1/logae=lna. Substituting this result into limΔx→0Δy/Δx=limΔx→0a^x(a^Δx-1)/Δx, we get limΔx→0Δy/Δx=a^xlna. It can be known that when a=e, y=e^x y'=e^x.

4. y=logax Δy=loga(x Δx)-logax=loga(x Δx)/x=loga[(1 Δx/x)^x]/x Δy/Δx=loga[(1 Δx/x)^(x/ Δx)]/x Because when Δx→0, Δx/x tends to 0 and x/Δx tends to ∞, so limΔx→0loga(1 Δx/x)^(x/Δx)=logae, so there is limΔx→0Δy /Δx=logae/x. You can also further use the base-changing formula limΔx→0Δy/Δx=logae/x=lne/(x*lna)=1/(x*lna)=(x*lna)^(-1). It can be known that when a=e Sometimes y=lnx y'=1/x. At this time, the derivation of y=x^n y'=nx^(n-1) can be carried out. Because y=x^n, so y=e^ln(x^n)=e^nlnx, so y'=e^nlnx·(nlnx)'=x^n·n/x=nx^(n-1 ). 5.y=sinx Δy=sin(x Δx)-sinx=2cos(x Δx/2)sin(Δx/2) Δy/Δx=2cos(x Δx/2)sin(Δx/2)/Δx=cos( x Δx/2)sin(Δx/2)/(Δx/2) So limΔx→0Δy/Δx=limΔx→0cos(x Δx/2)·limΔx→0sin(Δx/2)/(Δx/2)=cosx 6. Similarly, one can export y=cosx y'=-sinx. 7． y=tanx=sinx/cosx y'=[(sinx)'cosx-sinx(cosx)']/cos^2x=(cos^2x sin^2x)/cos^2x=1/cos^2x 8. y=cotx=cosx/sinx y'=[(cosx)'sinx-cosx(sinx)']/sin^2x=-1/sin^2x 9． y=arcsinx x=siny x'=cosy y'=1/x'=1/cosy=1/√1-sin^2y=1/√1-x^2 10. y=arosx x=cosy x'=-siny y'=1/x'=-1/siny=-1/√1-cos^2y=-1/√1-x^2 11. y=arctanx x=tany x'=1/cos^2y y'=1/x'=cos^2y=1/sec^2y=1/1 tan^2x=1/1 x^2 12. y=arotx x=coty x'=-1/sin^2y y'=1/x'=-sin^2y=-1/csc^2y=-1/1 cot^2y=-1/1 x^2 In addition, when deriving the derivatives of hyperbolic functions shx, chx, thx, etc. and inverse hyperbolic functions arshx, archx, arthx, etc. and other more complex composite functions, refer to the derivative table and use the formula at the beginning and 4. y=u soil v, y'=u' soil v' 5. y=uv, y=u'v uv' can obtain the result more quickly. For y=x^n y'=nx^(n-1), y=a^x y'=a^xlna has a more direct derivation method.

y=x^n It can be seen from the definition of exponential function that ygt; 0 takes the natural logarithm ln on both sides of the equation y=n*ln x Derive the derivative of x on both sides of the equation. Note that y is the composite function of y on x y' * (1/y)=n*(1/x) y'=n*y/x=n* x^n / x=n * x ^ (n-1) The power function can be proved in the same way as the derivative. In fact, it is the slope of the curve and the rate of change of the function value. The denominator mentioned above tends to zero. This is of course, but don’t forget that the numerator may also tend to zero, so the ratio of the two may be a certain number. , if the molecule tends to a certain number instead of zero, then the ratio will be very large and can be considered to be infinite, which means that the derivative we call does not exist. x/x, if X tends to zero here, the denominator will tend to zero, but their ratio is 1, so the limit is 1. It is recommended to first understand what a limit is. The limit is an elusive concept. You can get very close to it, but you will never reach the shore. And you must realize that the derivative is a ratio.

The function of the symbol '~' in matlab. Use it with examples and explain it. Thank you!

Whether it means 0,

For example, A=[1 0 3; 4 5 6; -7 8 0];

a=~A

a=[0 1 0; 0 0 0; 0 0 1]

" | " How to read this mathematical symbol, what does it mean, please give an example

| is used in probability,

For example: P(A|B), which indicates the probability of event A happening again under the condition that event B has occurred, which is called conditional probability; how to read it unclearly , maybe it’s called conditional probability or something

Please give an example of how to insert a background image into it?

To insert a background image, use background-image. For example, the code for inserting a background image into the entire page is as follows

lt;!DOCTYPE gt;lt;gt;lt;headgt;lt;meta charset=utf-8gt;lt;meta -equiv="X-UA-Compatible" content="IE=edge,chrome=1"gt;lt;titlegt;Exampleslt;/titlegt;lt;meta name=description content=" "gt;lt;meta name=keywords content=""gt;lt;link href=" " rel="stylesheet"gt;lt;style type=text/css media="screen"gt; body{ background-image: url(01.jpg); background-repeat: no-repeat; background-size: cover; }lt;/stylegt;lt;/headgt;lt;bodygt;lt;/bodygt;lt;/gt;

Please give an example of how to use the punctuation mark ","?

Example: Our favorite sports include basketball, football, volleyball and table tennis.

Mainly used to mention a series of similar things.

Please give an example of the use of callback functions in mfc?

Callback functions are not exclusive to MFC, and are also found in non-MFC. Sometimes setting callback functions actually means that you want a certain function to be called during the execution of a certain program, and The called function is customarily called a callback function, which is just a name. Every window program must fill in a window procedure function indicator when registering the window class. In fact, this window procedure function can also be called a callback. Functions are just called window procedures. For example, when writing a program to copy files, you can also set a callback function when calling the file copying function. Then the system will continuously call this callback function during the file copying process. One of the arguments of the function indicates how many bytes of data have been copied, so we can count how many bytes have been copied in the callback function. Based on the statistics, we can draw the file copy progress, etc., if not If you set a callback function, there is no chance to know the current copying progress during the copying process, because copying files only requires calling an API. Copying files is actually completed by the driver, and the API only sends a command to the driver.

The pronunciation, explanation and application of Yin Yun. Please give an example

氤氲: [ yīn yūn ]

yīnyūn

The appearance of smoke and smoke; the appearance of mixed turbulence of air or light

There are many beautiful colors in Lingshan, and the water in the sky is dense. ——Zhang Jiuling of the Tang Dynasty, "Wang Lushan Waterfall Spring at Hukou"

The clouds and smoke are dense and dense

The clouds and smoke are dense and dense

a. The smoke and clouds fill the air, like "there are many beautiful colors in the spiritual mountains, and the empty water is full~~"; b. A term in Chinese philosophy that refers to the change and growth of all things through interaction, such as "Heaven and earth~~, all things become mellow."

`Adjective` Because it has "the appearance of..." it is an adjective. It seems that relieved is an adjective, but sometimes it can be used as a verb