Why is 1 plus 1 equal to 2? Please use calculus to explain.

Why is 1 plus 1 equal to 2? Please explain calculus with calculus. Let me tell you: there is a melon baby in the class, then there is another melon baby, and finally there are two melon babies in the class.

Help me use calculus to explain why one plus one equals the limit of binary function. There are two forms: repeated limit and repeated limit.

Please ask specific questions.

Xy/sqrt (x 2+y 2), when x and y tend to the limit of 0.

Let x = rcosa and y = rsina.

X and y tend to 0, then r tends to 0.

xy=(r^2)*sina*cosa

sqrt(x^2+y^2)=r

Xy/sqrt (x 2+y 2), the limit when x and y tend to 0 is

R * Sina * cosa-& gt；; 0

Xy/sqrt (x 2+y 2), when x and y tend to 0, the limit is 0.

Why do you say 1+ 1=2? That warrior can use calculus to explain how to prove that 1 plus 1 equals 2. Chen Jingrun's proof is called Goldbach-Herschel conjecture. It is not to prove why the so-called 1+ 1 is equal to 2. In his letter to Euler, Goebbels said that he thought that any even number greater than 6 could be written as the sum of two prime numbers, but he could neither deny this proposition nor prove it correct. Euler can't prove it either. The sum of these two prime numbers is simply "1+ 1". Hundreds of years have passed, and no one can prove the Goldbach-hershey conjecture, including Chen Jingrun. He just took the proof a big step forward, but he still didn't fully prove it.

2

Why is 1+ 1 equal to 2? This question seems simple but wonderful. Axiomatic methods are widely used in modern precision science, especially in mathematics and mathematical logic. What is the law of justice? From many principles of a certain science, some basic concepts and propositions are separated. These basic concepts are undefined, and all other concepts of this discipline must be directly or indirectly defined by them. These basic propositions (also called axioms) have not been proved, but all other propositions of this discipline must be directly or indirectly derived from them. The theoretical system thus formed is called axiomatic system, and the method of forming this axiomatic system is called axiomatic method. 1+ 1=2 is an axiom in mathematics and needs no proof. And because 1+ 1=2 is the basis of all mathematical theorems, .........

Why do you say 1+ 1=2? That warrior can be explained by calculus. This belongs to piano's axiomatic system of natural numbers, and calculus is a real number system.

Anyone who has studied mathematics with calculus knows that it is much easier to calculate the length of a straight line than the length of a curve. In order to find the length of a curve, the curve is infinitely subdivided into several small straight lines, and then the length of these straight lines is added up to get the length of the curve. This idea is calculus in advanced mathematics.

What is calculus? Why is the cycle of 0.9 equal to 1 in calculus theory? The foundation of calculus is limit theory.

Generally speaking, the limit is: if you give me a positive number at will, I can give you a smaller one.

Strictly speaking, the limit is defined by a sequence, {Xn} is a real sequence, and A is a definite number. For any positive number ε, there is always a positive integer n, so when n >; ∣ xn-a ∣ < ε means that the sequence {Xn} converges to a, and the fixed number A is called the limit of the sequence {Xn}, which is recorded as

Xn→a(n→∞)

A cycle of 0.9 can be regarded as a sequence, xn = 0.9...9 (n 9s), and its limit is 1.

In calculus, 2x+ 1=u explains why dx= 1/2du uses differential properties, and d(2x+ 1)=d(u) means d(2x)+d 1=du means 2dx+0=du means dx =

When solving problems with calculus, let the acceleration be at least m/s 2.

100 km/h =100/3.6 m/s (I hate such complicated numbers ...)

The speed at deceleration is v= 100/3.6-at.

When the speed drops to v=0, the time taken is t= 100/3.6a (s).

Then when the car decelerates to 0, the distance traveled by the car is exactly 80m, so that accidents can be avoided. Velocity integral

So ∫ (100/3.6 -at)dt=80 (the integral t ranges from 0 to 100/3.6a).

This solution gives a = a = a=4.82 m/s^2 (approximately equal to).

In fact, this problem is very simple without calculus.

Why is the calculus dkt÷dt equal to 2kt? Wrong.

dkt/dt=k

dkt^2/dt=2kt

What is calculus? Please explain that calculus is a branch of mathematics, which studies the differential and integral of functions and related concepts and applications. Calculus is based on real numbers, functions and limits. The most important idea of calculus is to use "infinitesimal" and "infinite approximation", just like a thing is always changing, and you can't learn it well, but if you divide it into small pieces with infinitesimal, you can think of it as continuous processing and finally add it up.

Calculus is a general term for differential calculus and integral calculus. It is a mathematical idea, in which' infinite subdivision' is differential and' infinite summation' is integral. Infinity is the limit, and the thought of limit is the basis of calculus, that is, to look at problems with a moving thought. For example, the instantaneous speed of a bullet flying out of a gun bore is the concept of differentiation, and the sum of the distances traveled by a bullet at each instant is the concept of integration. If the whole mathematics is compared to a big tree, then elementary mathematics is the root of the tree, each branch of mathematics is the branch, and the main part of the trunk is calculus. Calculus is one of the greatest achievements of human wisdom.

The concepts of limit and calculus can be traced back to ancient times. In the second half of the 17th century, Newton and Leibniz completed the preparatory work that many mathematicians participated in, and independently established calculus. Their starting point of establishing calculus is intuitive infinitesimal, and their theoretical foundation is not solid. It was not until the19th century that Cauchy and Wilstrass established the limit theory, and Cantor and others established the strict real number theory that the discipline was rigorous.

Calculus is developed with practical application, and is more and more widely used in various branches of natural science, social science and applied science such as astronomy, mechanics, chemistry, biology, engineering and economics. In particular, the invention of computers is more conducive to the continuous development of these applications.

Everything in the objective world, from particles to the universe, is always moving and changing. Therefore, after introducing the concept of variables into mathematics, it is possible to describe the movement phenomenon in mathematics.

Due to the emergence and application of the concept of function and the needs of the development of science and technology, a new branch of mathematics has emerged after analytic geometry, which is calculus. Calculus plays a very important role in the development of mathematics. It can be said that it is the greatest creation in all mathematics after Euclidean geometry.

The establishment of calculus

Calculus became a discipline in the seventeenth century, but the idea of differential and integral existed in ancient times.

In the third century BC, Archimedes of ancient Greece implied the idea of modern integral calculus when he studied and solved the problems of parabolic arch area, spherical surface and spherical cap area, area under spiral, and volume of hyperbola of rotation. As the basis of differential calculus, limit theory has been clearly discussed as early as ancient times. For example, the book Zhuangzi written by Zhuang Zhou in China records that "one foot of space is inexhaustible." Liu Hui in the Three Kingdoms period mentioned in his "Cutting Circle" that "if you cut it carefully, you will lose less, and if you cut it again, you will not even lose your circumference and body." These are simple and typical limit concepts.

In the seventeenth century, there were many scientific problems to be solved, and these problems became the factors that prompted calculus. To sum up, there are mainly four kinds of problems: the first kind is the problem that appears directly when learning physical education, that is, the problem of finding the instantaneous speed. The second kind of problem is to find the tangent of the curve. The third kind of problem is to find the maximum and minimum of a function. The fourth problem is to find the length of the curve, the area enclosed by the curve, the volume enclosed by the surface, the center of gravity of the object, and the gravity of an object with a considerable volume acting on another object.

/kloc-many famous mathematicians, astronomers and physicists in the 0/7th century did a lot of research work to solve the above problems, such as Fermat, Descartes, Roberts and Gilad Girard Desargues. Barrow and Varis in Britain; Kepler in Germany; Italian cavalieri and others put forward many fruitful theories. Contributed to the creation of calculus.

/kloc-In the second half of the 7th century, Newton, a great British scientist, and Leibniz, a German mathematician, independently studied and completed the creation of calculus in their respective countries on the basis of their predecessors' work, although this was only a very preliminary work. Their greatest achievement is to connect two seemingly unrelated problems, one is the tangent problem (the central problem of differential calculus) and the other is the quadrature problem (the central problem of integral calculus).

Newton and Leibniz established calculus from intuitive infinitesimal, so this subject was also called infinitesimal analysis in the early days, which is also the source of the name of the big branch of mathematics now. Newton's research on calculus focused on kinematics, while Leibniz focused on geometry.

Newton wrote Flow Method and Infinite Series at 167 1, and it was not published until 1736. In this book, Newton pointed out that variables are produced by the continuous motion of points, lines and surfaces, and denied that variables are static sets of infinitesimal elements. He called continuous variables flow, and the derivatives of these flows were called flow numbers. Newton's central problems in flow number technology are: knowing the path of continuous motion and finding the speed at a given moment (differential method); Given the speed of motion, find the distance traveled in a given time (integral method).

Leibniz of Germany is a knowledgeable scholar. 1684, he published what is considered to be the earliest calculus literature in the world. This article has a long and strange name: a new method for finding minimax and tangents, which is also applicable to fractions and irrational numbers, and the wonderful types of calculation of this new method. It is such a vague article, but it has epoch-making significance. He is famous for containing modern differential symbols and basic differential laws. 1686, Leibniz published the first document on integral calculus. He is one of the greatest semiotics scholars in history, and his symbols are far superior to Newton's, which has a great influence on the development of calculus. Leibniz carefully chose the universal symbol of calculus that we use now.

The establishment of calculus has greatly promoted the development of mathematics. In the past, many problems that elementary mathematics was helpless were often solved by calculus, which shows the extraordinary power of calculus.

As mentioned above, the establishment of a science is by no means a person's achievement. It must be completed by one person or several people through the efforts of many people and on the basis of accumulating many achievements. So is calculus.

Unfortunately, while people appreciate the magnificent function of calculus, when they put forward who is the founder of this subject, it actually caused a blatant * * *, which caused a long-term opposition between European mathematicians and British mathematicians. British mathematics was closed to the outside world for a period of time, limited by national prejudice, and too rigidly adhered to Newton's "flow counting", so the development of mathematics fell behind for a whole hundred years.

In fact, Newton and Leibniz studied independently, and completed them in roughly the same time. More specifically, Newton founded calculus about 10 years earlier than Leibniz, but Leibniz published calculus theory three years earlier than Newton. Their research has both advantages and disadvantages. At that time, due to national prejudice, the debate about the priority of invention actually lasted from 1699 to 100 years.

It should be pointed out that this is the same as the completion of any major theory in history, and the work of Newton and Leibniz is also very imperfect. They have different views on infinity and infinitesimal, which is very vague. Newton's infinitesimal, sometimes zero, sometimes not zero but a finite small amount; Leibniz's can't justify himself. These basic defects eventually led to the second mathematical crisis.

Until the beginning of19th century, the scientists of French Academy of Sciences, led by Cauchy, made a serious study of the theory of calculus and established the limit theory, which was further tightened by the German mathematician Wilstrass, making the limit theory a solid foundation of calculus. Only in this way can calculus be further developed.

Any emerging and promising scientific achievements attract the vast number of scientific workers. In the history of calculus, there are also some stars: Swiss Jacques Bernoulli and his brothers johann bernoulli, Euler, French Lagrange, Cauchy …

Euclidean geometry and algebra in ancient and medieval times were constant mathematics, and calculus was the real variable mathematics, which was a great revolution in mathematics. Calculus is the main branch of higher mathematics, and it is not limited to solving the problem of variable speed in mechanics. It gallops in the garden of modern science and technology and has made countless great achievements.

Basic content of calculus

It is the basic method of calculus to study the function and motion changes of things from the quantitative aspect. This method is called mathematical analysis.

Originally, mathematical analysis in a broad sense included many branches such as calculus and function theory, but now it is widely used to equate mathematical analysis with calculus, and mathematical analysis has become synonymous with calculus. When it comes to mathematical analysis, known refers to calculus. The basic concepts and contents of calculus include differential calculus and integral calculus.

The main contents of differential calculus include: limit theory, derivative, differential and so on.

The main contents of integral include definite integral, indefinite integral and so on.

Calculus is developed in application. At first, Newton used calculus and differential equations to deduce Kepler's three laws of planetary motion from the law of universal gravitation. Since then, calculus has greatly promoted the development of mathematics, as well as astronomy, mechanics, physics, chemistry, biology, engineering, economics and other natural sciences, social sciences and applied sciences. And it is widely used in these disciplines, especially the appearance of computers is more conducive to the continuous development of these applications.

Unary differential

Definition: Let the function y = f(x) be defined in a certain interval, and both x0 and x0+δ x are in this interval. If the increment of the function Δ y = f (x0+Δ x)? F(x0) can be expressed as Δ y = a Δ x0+o (Δ x0) (where a is a constant unrelated to Δ x), and o (Δ x0) is infinitely less than Δ x, then the function F(x) is said to be differentiable at point x0, and a Δ x is called the differential of the function at point x0 corresponding to the increment Δ x of the independent variable, which is denoted as dy, that is, dy =.

Usually, the increment Δ x of the independent variable X is called the differential of the independent variable, which is denoted as dx, that is, dx = Δ x. Then the differential of the function y = f(x) can be written as dy = f'(x)dx. The quotient of the differential of the function and the differential of the independent variable is equal to the derivative of the function. Therefore, the derivative is also called WeChat business.

Geometric meaning

Let Δ x be the increment of point m on the curve on the abscissa y = f(x), Δ y be the increment of the curve on point m corresponding to Δ x on the ordinate, and dy be the increment of the tangent of the curve on point m corresponding to Δ x on the ordinate. When | Δ x | is small, |Δy-dy | is much smaller than |Δy-dy | (high-order infinitesimal), so we can use a tangent line segment to approximate the curve segment near point M.

Multivariate differential

Similarly, when there are multiple independent variables, the definition of multivariate differential can be obtained.

Integration is the inverse operation of differentiation, that is, knowing the derivative function of a function and finding the original function in reverse. In application, the function of integration is not only this, but also widely used in summation, that is, to find the area of curved triangle. This ingenious solution is determined by the special properties of integral.

The indefinite integral of a function (also known as the original function) refers to another family of functions, and the derivative function of this family of functions is just the previous function.

Where: [F(x)+C]' = f(x)

The definite integral of a real variable function in the interval [a, b] is a real number. It is equal to the value in B minus the value in A of an original function of this function.