Calculus is used The moving distance of an object is x (meters), the function is x = sin (T), and t is the moving time of the object (seconds). What is its speed at π / 2 seconds The moving distance of an object is x (meters), the function is x = sin (T), and t is the moving time of the object (seconds). What is its speed at π / 2 seconds

Calculus is used The moving distance of an object is x (meters), the function is x = sin (T), and t is the moving time of the object (seconds). What is its speed at π / 2 seconds The moving distance of an object is x (meters), the function is x = sin (T), and t is the moving time of the object (seconds). What is its speed at π / 2 seconds

v(t)=dx/dt=cos(t)
When t = π / 2, bring in the above formula
v=0

Ask a very basic question about calculus That's it. I know that the value of C / ∞ tends to 0. The teacher told me that LIM (x tends to ∞) SiNx / x = 0, not 1, because SiNx is bounded. So does C need to be a constant? As long as it is a bounded function, C / ∞ tends to 0? You'd better give an example to help me understand it

Yes, it can be understood in two ways
1. Bounded times infinitesimal (one part of infinity is infinitesimal of course). This is the theorem
2. According to the usual idea, as long as the molecule is bounded, whether it is a function or a constant, the boundedness of its value is that the absolute value of the function value is less than or equal to a value, and the constant will not increase infinitely. Of course, dividing a certain large number by an infinite number is infinite and tends to 0, that is, the limit is 0

Ask a basic problem of calculus When calculating the area by integration, the teacher said that after dividing a curved trapezoid into many small curved trapezoids, the area △ s ≈ f (x) DX of each small curved trapezoid (because DX is set as the interval length) Then, the teacher said that this is only about equal, and there is a high-order infinitesimal difference between them. Then he said that DS = f (x) DX becomes an equal sign and called it an area element. I don't know what a high-order infinitesimal is here. Why can it become an equal sign by adding d before s?

F (x) DX is the sign of calculus. When the interval tends to infinity, the area changes from about equal to equal to
Advanced infinitesimal high school can understand it as taking the limit. You will learn more about calculus in college. Then you will know

Make all lines at a point a on the curve y = x (x is greater than or equal to 0), so that the area enclosed by the curve and X axis is 1 / 12 Find the coordinates of tangent point a and tangent equation

Let a (a, a * a)
The tangent equation passing through point a is y = 2ax-a * a, and the intersection with y axis is (A / 2,0)
The third power of a / 3 - (A-A / 2) * a * A / 2 = 1 / 12
a=1
That is, a (1,1), the tangent equation is y = 2x-1

A calculus problem Find ∫ (2x + 3) / (x ^ 2 + 2x + 2) DX

∫（2x+3）/（x^2+2x+2）dx
=∫（2x+2）/（x^2+2x+2）dx+∫1/（x^2+2x+2）dx
=∫d（x^2+2x+2）/（x^2+2x+2）+∫1/[(x+1)^2+1]dx
=ln(x^2+2x+2)+arctan(x+1)+C

Help, a calculus problem Try to determine the values of constants a, B and C so that e ^ x (1 + BX + CX ^ 2) = 1 + ax+ ο (x ^ 3), where ο (x ^ 3) is the higher-order infinitesimal when x → 0

Hello!
When x → 0,
e^x = 1+x+ x ²/ 2 + x ³/ 6……
e^x(1+Bx+Cx ²)
=[1+x+ x ²/ 2 +x ³/ 6 ……](1+Bx+Cx^2)
=1+x+ x ²/ 2 + x ³/ 6……+Bx+Bx ²+ Bx ³/ 2+…… Cx ² + Cx ³+……
= 1+(B+1)x +(1/2+B+C)x ² + (1/6 + B/2 +C)x ³ +ο (x ³)
= 1+Ax+ ο (x ³)
∴B+1=A,1/2 +B+C=0,1/6 +B/2 +C =0
The solution shows that a = 1 / 3, B = - 2 / 3, C = 1 / 6