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

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• 1. Why is the proposition "when limx →∞ f (x) = 0, there is x > 0, when x > x, f (x) is bounded" wrong?
• 2. 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).
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• 6. 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
• 7. 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
• 8. 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
• 9. If y = f (x) is a differentiable function and f '(1) = 2, then when x = - 1, the derivative value of function f (- x) is the solution
• 10. The function f (x) = AX3 + 3x2 + 2, if f '(- 1) = 4, then the value of a is equal to______ ．
• 11. 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
• 12. 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
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• 16. 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)
• 17. 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)
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• 19. 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
• 20. 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