What's the integral of 1 / X & sup2;? What's the integral of 1 / x square? What's the integral of 1 / X LNX? What's the integral of 1 / X & sup2? It's - 1 / x + C

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• 1. lim(x→1)(x^2-2x+1)/lnx-x+1
• 2. LIM (x approaches infinity) √ (the square of x-3x) / 2x + 1 How to do it
• 3. On the theorem of infinitesimal and infinitesimal For example, theorem: the sum of finite infinitesimals is also infinitesimal Suppose that when x tends to x0, it is proved in the book that the sum of two infinitesimals when x tends to x0 satisfies the condition of infinitesimal But I think, why do two infinitesimals just tend to x0 when proving? The theorem says that two infinitesimals do not necessarily have the same x0? For example, the x power of (0.5) and the x power of 2 are infinitesimal. Although these two functions are not infinitesimal when they tend to finite values, their sum will not be infinitesimal Why?
• 4. Limx → 0sin3x / sin5x, find the limit
• 5. Find the limit: limx (1 + 2x) &# 185; divide by the square of X, when x approaches 0, how to find it,
• 6. It is proved that the function y = (1 / x) sin (1 / x) is unbounded in the interval (0,1], but it is not infinite when x tends to positive infinity
• 7. Let f (x) = | x-1| Tan (x-3) / (x-1) (X-2) (x-3) ^ 2, then f (x) is bounded a (0,1) B (1,2) C (2,3) d (3,4) in which of the following intervals
• 8. Higher numbers, on equivalent infinitesimals LIM (x approaches 0) 1 / (1-cosx) + 1 / TaNx Can TaNx, (1-cosx) be replaced by the equivalent infinitesimal? If not, why not, can not all multiplication and division be used? 2. LIM (x approaches infinity) [E / (1 + 1 / x) ^ x] ^ x Can (1 + 1 / x) ^ X be replaced by e? If not, why not?
• 9. A higher number problem on the Equivalent Infinitesimal Substitution limx→0（sinx-tanx)/{[3√(1+X^2)-1][(1+sinx)-1]} Can the denominator be replaced by "x ^ 2 / 3" and "SiNx / 3" with the equivalent infinitesimal? Because the two equivalent infinitesimals are the same, the subtraction of the molecular part cannot be replaced, so the following steps are not very clear,
• 10. On the replacement of equivalent infinitesimal There is a saying in the book: when calculating the limit of the ratio of two infinitesimals, the product factor of the numerator or denominator can be replaced by its equivalent infinitesimal. First, what is the product factor? For example: limx → 0 (e ^ AX-1 + e ^ BX-1) / 2x, can the numerator replace ax BX? It seems that this is not the product factor
• 11. Limit: when x tends to positive infinity, does the limit of function f (x) = LNX ax tend to negative infinity;
• 12. Find the limit of function (x / x-1) - (1 / LNX) x tending to 1
• 13. What is the power of infinitesimal to infinity? 0^∞ =0
• 14. What is infinity divided by infinitesimal
• 15. What is infinity plus infinitesimal For example, LIM (x →∞) (1 / x + e ^ x). It can be seen from the graph that it is infinite, or it can also be known that it is infinite by taking in the number to calculate, but how to solve this problem, In addition, LIM (x → - ∞) (1 / x + e ^ x)
• 16. What is the infinite power of E?
• 17. Is the positive infinity power of a number less than one and greater than 0 equal to 0
• 18. When x → 0, α (x) = kx2 and β (x) = 1 + xarcsinx − cosx are equivalent infinitesimals, then K=______ ．
• 19. Use the property of infinitesimal to calculate the following limit (1) Limx ^ 2cos1 / x where x tends to 0 (2) Lim [(arctanx) / x] where x tends to infinity
• 20. Is it right to say that the limit of infinitesimal is 0?