Solving the limit of (1 + SiNx) ^ Cotx when x approaches 0

The limit value is (1 + cos0) ^ (- sin0) = 2 ^ 0 = 1

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1. If the non-zero function f (x) has f (a + b) = f (a) * f (b) for any real number a and B, and if X1 proves: F (x) > 0
2. If the nonzero function f (x) has f (a + b) = f (a) &; f (b) for any real number A.B, and if x1, (1) prove that f (x) > 0 (2) prove that f (x) is a decreasing function (3) solve the inequality f (x-3) &; f (6-2x) ≤ 1 / 4 when f (4) = 1 / 16
3. If both non-zero real numbers a and B have f (a + b) = f (a) * f (b) and if x 1, we prove that f (x) is a decreasing function
4. Why is the proposition "when limx →∞ f (x) = 0, there is x > 0, when x > x, f (x) is bounded" wrong?
5. F (0) = f (1) = 0, f (1 / 2) = 1. It is proved that there is at least one point in (0,1) such that f '(x) = 1 F (x) is continuous on [0,1] and differentiable in (0,1).
6. If f (x) = 2x + 1 and X is not equal to 1, find limf (x) (x tends to 1) and prove it by using ε - δ I don't know much about this
7. Let f (x) = {X-1, X ≥ 1, x, - 1
8. Given that the function y = FX defined on R satisfies f (2 + x) = 3f (x), when x ∈ [0,2], f (x) = x-2x, find f (x) when x ∈ [- 4, - 2]=
9. The derivative value of the differentiable function y = f (x) at one point is 0, which is the extreme value of the function y = f (x) at this point () A. Sufficient condition B. necessary condition C. necessary and insufficient condition D. sufficient and necessary condition
10. The derivative value of the differentiable function y = f (x) at one point is 0, which is the extreme value of the function y = f (x) at this point () A. Sufficient condition B. necessary condition C. necessary and insufficient condition D. sufficient and necessary condition
11. lim/(x→0)⁡3*sinx/x=
12. Given f (x) = (1 + x) / sinx-1 / x, let a = Lim f (x) be the value of A Given f (x) = (1 + x) / sinx-1 / x, note a = LIM (x → 0) f (x) 1. Find the value of A. answer: the value of a is 1.2. If x → 0, f (x) - A is the infinitesimal of x ^ k of the same order, find the value of constant K
13. If f (x) has second derivative in the field of x = 0, and if x → 0, LIM ((SiNx + XF (x)) \ \ x3) = 0, find f (0), f '(0), f' '(0)
14. If f (x) has a second derivative in the field of x = 0, and if x → 0, LIM ((SiNx + XF (x)) \ \ x3) = 1 / 2, find f (0), f '(0), f' '(0)
15. LIM (x-sinx) / XLN (1 + x ^ 2) x tends to 0
16. Calculus: Lim [(x ^ 3-x ^ 2 + X / 2) e ^ 1 / X - (x ^ 6 + 1) ^ 1 / 2] x → + ∞ It's going to be done with Taylor's remainder
17. Calculus problem, given f (0) = 0, f '(0) = 1, f' '(0) = - 2, find LIM (x → 0) (f (x) - x) / x ^ 2 =? Given that f (0) = 0, f '(0) = 1, f' '(0) = - 2, find LIM (x → 0) (f (x) - x) / x ^ 2 =? For detailed explanation
18. Calculus problem, known Lim x → 0 f (x) / x ^ 2 = 1, find Lim x → 0 f (x) =? And then find Lim x → 0 f (x) / x =? The main problem lies in LIM x → 0, x ^ 2 = 0, and it is in the denominator position, so we can not directly think that f (x) = x ^ 2
19. When x approaches to 0, find the limit value of LIM (1-sinx) ^ 1 / X Very urgent, to detailed steps, trouble you The answer must be right!!
20. According to LIM (SiNx / x) = 1, find LIM (tan2x / x) =? X approaches 0, x approaches 0