It is proved that the function y is uniformly continuous in the finite open interval (a, b), then it is bounded in this interval

Word limit, abbreviated
Let ε = 1, there exists δ > 0, for X ', X' '∈ (a, b), when 0

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1. It is proved that if f (x) is differentiable on the interval I and the derivative function on I is bounded, then f (x) is uniformly continuous on I
2. Let f (x) and G (x) be bounded on D. It is proved that f (x) + G (x), f (x) - G (x), f (x) * g (x) are also bounded on D There is another proof that the function y = xsinx is unbounded on (0, + 8), that, + 8 is positive infinity
3. What is the derivative of logx?
4. F (x) = logx / X for the first and second derivatives Dizzy.. Every answer is heavy.
5. What is the derivative of the derivative of F (x) = log (4x logx)
6. What is the derivative of logx ^ 2? What is the result of deriving logx ^ 2
7. It is proved that the derivative of F (x) * LNX + F (x) * (2 / x) = 0
8. Let g (x) = {① e ^ x, X ≤ 0, ② LNX, x > 0, then the solution set of inequality g (x) ≤ 1 about X is () A.（-∞,1] B.(-∞,e] C.[o,e] D.[0,1]
9. Proof: when x > 0, the inequality LNX > = 1-1 / X
10. Proving: inequality 1 / lnx-1 / (x-1)
11. How to prove that a function is bounded in an interval
12. If f (x) is known to be a differentiable function, then Lim △ x → 0 f ^ 2 (x + △ x) - f ^ 2 (x) / △ x =?
13. Let f '(x) = f (x), f (x) be a differentiable function, f (0) = 1, and f (x) = XF (x) + x ^ 2, find f' (x) and f (x)
14. F (x) is a differentiable function defined on (0, + ∞) and satisfies XF '(x) - f (x) a
15. If e ^ x is a primitive function of F (x), then ∫ XF (x) DX limit
16. If the differentiable function f (x) defined on (0, + ∞) satisfies: X · f '(x) < f (x) and f (1) = 0, then the solution set of F (x) x < 0 is () A. （0，1）B. （0，1）∪（1，+∞）C. （1，+∞）D. ϕ
17. This paper discusses the limit of function f (x) = | x | / X when x tends to 0 Use piecewise function, be specific
18. The derivative function f '(x) of function f (x) is continuous, and f (0) = 0, f' (0) = A. note that the nearest point of curve y = f (x) and P (T, 0) is Q (s, f (s)), and find the limit value Lim s / T (when t tends to 0)
19. Let f (x) be differentiable at x = 0, and f (0) = 0, then find the following limit, where a is not equal to 0 and is a constant lim x→0 [ f(ax)-f(-ax)]/x
20. If the function f (x) is differentiable at x = 0, and f (0) = 0, X tends to 0: then find the limit f (x) / x =?