Find the absolute value of two limits x divided by X (x tends to 0) (x tends to 0 +)!

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• 1. The limit of absolute value As follows: lim│x│ ( x→0)
• 2. Let the function y = f (x) have a third order continuous derivative in a neighborhood of x = x0. If f "(x0) = 0 and F" '(x0) is not equal to 0, ask the relation between F' (x0) and 0,
• 3. Let f (x) be continuous on [0,1] and f (0) = f (1). It is proved that there must be XO ∈ [0,1 / 2] such that f (XO) = f (XO + 1 / 2)
• 4. Proof: F (x) is monotonically increasing, if there is {xn} - > + ∞, such that limf (xn) = a (n - > ∞), then limf (x) = a (x - > ∞) It is proved that let limf (xn) = a For any E > 0, there exists N1 such that | f (xN1) - a | + ∞, there exists a natural number n. when n > N, there is xn > xN1 Then | f (xn) - f (xN1) | ≤ | f (xN1) - A| The last step is to use Heine's theorem
• 5. Let f (x) be differentiable at XO, then LIM (x) approaches 0, f (XO + x) - f (xo-3x) / X is equal to 0 A.2f'(xo) B.f'(xo) C.3f'(xo) D.4f'(xo）
• 6. Let the function FX be differentiable at point X and find the following limit. Limf (x + α h) - f (x - β h) / h, (α, β are constants)
• 7. If the function f (x) is differentiable at point XO, then f (x) is continuous at point XO Prove the above proposition
• 8. Seek master second solution high number problem, logarithm derivation Logarithm derivation, known function y = x one of the x power, X is greater than 0, find the derivative of Y
• 9. Simplification of logarithm How to change x ^ lgx + 2 = 1000 to (lgx + 2) lgx = 3
• 10. On logarithm, exponential operation, a+lga=10 b b+10 =10 Find a + B How to draw a picture
• 11. The absolute value of X-1 is divided by the limit of X-1
• 12. The same Heine's theorem proves that cos (1 / x) = 1 does not exist when LIM (x tends to 0)
• 13. Limx / (- x + x), when x tends to zero, does the limit exist? If it exists, what is it? If not, why not?
• 14. The differentiability and continuity of function f (x) = | cosx | are discussed
• 15. Given the function f (x) = | x | + 1, we study the continuity and differentiability of F (x) at x = 0
• 16. To prove the continuity of a function, is it possible to determine the continuity of a function in an interval as long as the continuity of two endpoints is proved (in an open and closed interval)?
• 17. The proof of function continuity Given that f (x) and G (x) are continuous at x0, it is proved that h (x) = max (f (x), G (x)) is continuous at x0
• 18. Continuity of piecewise function  
• 19. What is the definition of function continuity? How to judge whether a function is continuous?
• 20. Discuss the continuity of function This paper discusses the continuity of function f (x) = LIM (1-x ^ 2n / 1 + x ^ 2n) X. if there are discontinuities, the type of discontinuities is determined n→∞ In the given answer, f (x) = - x | x | > 1 0 |x|=1 x |x|