It is known that the derivative of F (x) at x = x0 is 4, Lim [x → x0] [f (x) - f (x0)] / 2 (x0-x)]=_______

RELATED INFORMATIONS

• 1. When h approaches 0, Lim H / F (A-H) - f (a) = 1 / 3, then the derivative of F (a) is
• 2. Let the function y = f (x) be defined in a certain interval, where x0 and x0 + Δ X are defined. What do x0 and x0 + Δ x mean
• 3. Given the function f (x) = x * 3-x * 2 + X / 2 + 1 / 4, it is proved that there exists x0 belonging to 0 to 1 / 2, such that f (x0) = x0
• 4. A necessary and sufficient condition for a function f (x) to be differentiable at point x0 is that the left and right derivatives of F (x) at point x0 exist and are equal. / / / / / / / / / / / / / / however, a necessary condition for differentiability is continuity. Is this contrary to the first proposition
• 5. For example, the derivative of continuous function is not necessarily continuous F (x) is differentiable everywhere on (a, b), but there exists x0 ∈ (a, b), so that f '(x0) exists, but f' (x) is discontinuous at x0 Who can give such an example?
• 6. On the problem of function differentiability, is it required that the left and right derivatives are equal and equal to the derivatives at x0? Or is it only necessary that the left and right derivatives are equal? Or if it is a removable discontinuity point, it means that this derivative does not exist, but this derivative is differentiable?
• 7. Why is the derivative of a function at x0 not equal to the limit value of its derivative at x0
• 8. Let f (x) be second-order differentiable on [a, b], and f ″ (x) ＜ 0. It is proved that: ∫ BAF (x) DX ≤ (B-A) f (a + B2)
• 9. If f (x) is differentiable on R and has two real roots, it is proved that its derivative has at least one real root; if f (x) has three real roots, it is proved that its second derivative has better one real root Urgent request
• 10. F (x) has a second derivative at point x = 0, What does f (x) prove to be n-order differentiable (n > = 2) at x = a
• 11. Given that f (x) is differentiable at x0, then when h approaches 0, f (x0 + H) − f (x0 − h) 2H approaches () A. 12f′(x0)B. f′（x0）C. 2f′（x0）D. 4f′（x0）
• 12. Let f (x) be differentiable at x0, then it is equal to Why Lim f (x + H) - f (X-H) / h = 2F '(x) Why 2F '(x), not 1 / 2 F' (x) F '(x) isn't that 2 in the denominator, and it becomes 1 / 2 after it is put forward?
• 13. Lim x tends to 0 arcsin2x / sin3x
• 14. X tends to 0) Lim [(x + 4) ^ 1 / 2-2] / sin3x
• 15. Let f (x) be differentiable in a neighborhood of x = 0, and lim f '(x) = 1, then f (x) has extremum in x = 0, and the detailed solution is obtained
• 16. Let f (x) be differentiable and find Lim [f (x + △ x)] ^ 2 - [f (x)] ^ 2 △ x → 0 lim [f(x+△x)]^2-[f(x)]^2 △x→0 =lim{[f(x+△x)+f(x)]*[f(x+△x)-f(x)]}/△x Why is it equal to ＝2f(x)lim[f(x+△x)-f(x)]/△x Especially why is it equal to 2F (x) Please give specific reasons,
• 17. Let f (x) be differentiable at point X. = 0, and f (0) = 0 and f '(0) = 3, then the value of LIM (x →∞) [f (x) / x] ()
• 18. Given that f (x) is differentiable at x = 0, f (0) = 0, f '(0) = 2, what is the limit of F (sin3x) / X when x approaches 0
• 19. Let f (x) be differentiable on [0,1], and f (1) = 2 ∫ 0 ~ 1 / 2 XF (x) DX. It is proved that there exists ξ belonging to (0,1), such that f (ξ) + ξ f '(ξ) = 1
• 20. It is proved that LIM (1-e ^ 1 / x) / (1 + e ^ 1 / x) does not exist when x tends to 0 LIM (1 / X of 1-e) / (1 / X of 1 + e) does not exist when x tends to zero