![](data:image/svg+xml;utf8,<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" viewBox="0 0 72 71" width="72"></svg>)
Composite function f (x) = x ^ 2Sin (1 / x) (x > 0) f (x) = 0 x
f'(0)=lim[x^2sin(1/x)-f(0)] /(x-0)
=lim[x^2sin(1/x)] /x
=limxsin(1/x)
=0
So it's differentiable and its derivative is zero
This problem needs to be done by definition
It only shows that the derivative is discontinuous at x = 0, but it can't show that the derivative doesn't exist
The sum of abscissa of all intersection points of image of function y = 11 − X and image of function y = 2Sin π x (- 2 ≤ x ≤ 4) is equal to ()
A. 2B. 4C. 6D. 8
The image of the function Y1 = 11 − x, y2 = 2Sin π X has a common center of symmetry (1,0). When 1 < x ≤ 4, Y1 < 0 and Y2 has an image of 1.5 cycles on (1,4), it is a decreasing function on (1,32) and (52,72); it is an increasing function on (32,52) and (72,4)
The sum of abscissa of all intersection points of the image of function y = 1 / X-1 and the image of function y = 2Sin π x (- 2 ≤ x ≤ 4) is? Hope the answer is clear and easy to understand, thank you
Well, it would be better to have a picture
The answer is 8, please.
Function y = 1 / (x-1) and function y = 2Sin π x (- 2 ≤ x ≤ 4) let t = X-1, then x = 1 + T, t ∈ [- 3,3], function y = 1 / (x-1) and function y = 2Sin π x, that is, y = 1 / T and y = 2Sin π (1 + T) = 2Sin (π + π T) = - 2Sin (π T), t ∈ [- 3,3], because y = 1 / T and y = - 2Sin π T are odd functions and definite
RELATED INFORMATIONS
- 1. Let f (x) = {x ^ 2, X ≤ 1; ax + B, x > 1} to make f (x) continuous and differentiable at x = 1, what values should a and B take?
- 2. The known function f (x) = 2Sin (AX - π / 6) sin (AX + π / 3)
- 3. Given the function f (x) = 2Sin (2x + 30 °) + A + B + 1 (a > 0), when x is 0 to 90 °, the function value is [- 4, Please, big brother and big sister
- 4. The difference between the proof of continuity and uniform continuity of function
- 5. Discuss the continuity of function This paper discusses the continuity of function f (x) = LIM (1-x ^ 2n / 1 + x ^ 2n) X. if there are discontinuities, the type of discontinuities is determined n→∞ In the given answer, f (x) = - x | x | > 1 0 |x|=1 x |x|
- 6. What is the definition of function continuity? How to judge whether a function is continuous?
- 7. Continuity of piecewise function
- 8. The proof of function continuity Given that f (x) and G (x) are continuous at x0, it is proved that h (x) = max (f (x), G (x)) is continuous at x0
- 9. To prove the continuity of a function, is it possible to determine the continuity of a function in an interval as long as the continuity of two endpoints is proved (in an open and closed interval)?
- 10. Given the function f (x) = | x | + 1, we study the continuity and differentiability of F (x) at x = 0
- 11. Given the function f (x) = SiNx, x < and = 0, X is not equal to 0, x > 0, then f (0) =?
- 12. Let f (x) = {(x ^ a) sin [1 / (x ^ b)], X not equal to 0.0, x = 0.} when a, B take what value, f (x) is continuous at x = 0?
- 13. The function FX = x / (x-a) x is not equal to a, if a = - 2, it is proved that f (x) increases monotonically in (negative infinity, - 2)
- 14. Let f (x), X belong to R, X is not equal to 0, for any non-zero real number x, y, satisfy f (XY) = f (x) + F (y), find f (1), f (- 1)
- 15. If f (1-cosx) = sin ^ x, what is f (3 / 2) equal to
- 16. Let f (x) = x * sin (1 / x), X not equal to 0; when x equals 0, f (x) = 0, then why is the function continuous but not differentiable at x = 0 Or continuously differentiable, but how to prove it
- 17. F (x) = | X-2 |, what is the derivative at point x = 2, or does it not exist?
- 18. The derivative of F (x) = x ^ (4 / 5) - x ^ (9 / 5) does not exist when x =?
- 19. Why does the function y = | x | have no derivative in x = 0?
- 20. Given the function f (x) = 2x-1, what is f '(0) equal to