It is proved that the limit of 2 ^ (1 / x) when x tends to 0 - is 0?

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• 1. It is proved that the value of X (x + 1) (x + 2) (x + 3) + 1 is a complete square expression Try to be quick
• 2. The function f (x) is defined at x = 1. What is the condition for the existence of LIM (x tends to 1) f (x)? Just say that it is sufficient or necessary, or it is neither sufficient nor necessary,
• 3. Given the vector a = (2cosx, 1), B = (cosx, root 3sin2x-1), Let f (x) = vector a * vector B, where x ∈ R (1) find the minimum positive period of the function And monotone increasing interval
• 4. Find Lim [x tends to infinity] {(x ^ 3) * ln [(x + 1) / (x-1)] - 2x ^ 2}, the answer is 2 / 3,
• 5. LIM (when x tends to infinity) x ^ 2 [1-cos (1 / x)]
• 6. Lim when x tends to positive infinity, ln (x / 1 + x) =? Explain, thank you!
• 7. Find the limit LIM (x tends to be positive infinity) ln (2x) / ln (x)
• 8. Limx [ln (x + 1) - LNX] (x tends to positive infinity)
• 9. Graphic description: when x tends to 0, the absolute value of LIM X does not exist
• 10. Find the limit of the absolute value x of LIM divided by X
• 11. If the spring can change suddenly, it means that there is displacement in the limit time, X / T = V (time limit), and the pushing speed is infinite (but the speed cannot be infinite) But if one end of the spring is not connected with a mass object, the deformation of the light spring does not need time, can the elastic force change suddenly?
• 12. Bolzano Weierstrass theorem. Does this theorem have a Chinese name?
• 13. Who can help me prove the boundedness of function and the maximum and minimum theorem The property theorem of continuous function on closed interval: the continuous function on closed interval is bounded on the interval, and it must be able to obtain its maximum and minimum value. This theorem is easy to understand with graph, I hope someone can prove it with mathematical language,
• 14. Fixed value theorem of continuous function Let f (x) be continuous on a closed interval [1,3] (1) If f (1) + F (2) + F (3) = 3, try to prove that there is at least one point a on [1,3] so that f (a) = 1
• 15. Let y = f (x) be a decreasing function defined on (0, positive infinity) and satisfy f (XY) = f (x) + F (y), f (1 / 3) = 1, (1) Find the value of F (1); (2) If there is a real number m such that f (m) = 2, find the value of M; (3) If f (x) + F (2-x)
• 16. What is the limit of the function f (x) = sgnx x → 0?
• 17. The limit of function f (x) = | x | / X at x = 0
• 18. If the function f (x) has a limit at X., then f (x) is at x = X A may not define B continuous C differentiable D discontinuous
• 19. The limit of function f (x) = 2 ^ (1 / x) at x = 0 Explain the left and right limits
• 20. Does the function f (x) = (- 1) ^ X have a limit