Infinitesimal of higher number and limit problem When X - > 0, e ^ (x ^ 2) - cosx is () A. Higher order infinitesimal B. equal order but not equivalent infinitesimal C. lower order infinitesimal D. equivalent infinitesimal

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• 1. The sum of infinitesimal functions may be infinitesimal functions, or functions whose limit is constant So is it possible to get an infinite function? If so, please give a counter example If not, please give me the reason Please pay attention to the tone when answering. I'm very vulnerable and can't stand being told that I'm stupid Note: the function independent variable tends to a certain point
• 2. As far as I know, we use the ratio limit of two infinitesimals to reflect the speed of two infinitesimals approaching zero. When their ratio limit is equal to - 1, is it equivalent? For example, when x → 0, X and - X are infinitesimals, and the limit of their ratio is equal to - 1, so they tend to zero at the same speed. Theoretically, they are equivalent, but the equivalent definition of Infinitesimal in advanced mathematics textbooks is that the ratio limit is equal to 1, not the absolute value of the ratio limit is equal to 1
• 3. The reciprocal of infinity is infinitesimal, and the reciprocal of constant not zero is infinity period Can you make it clear why it is a variable
• 4. The reciprocal of infinitesimal is infinity. How to understand it? For example, LIM (x ^ 2 + 2x-3) / (4x-1) = 0, why is its reciprocal infinite? This function is not always nonzero n-1
• 5. Is limit equal to infinity the existence or non existence of limit?
• 6. Does limit infinity and infinitesimal exist
• 7. Limit problem the problem of infinity and infinitesimal Please give examples to illustrate that the following three propositions are wrong 1. The product of infinitesimals is infinitesimal 2. Infinity plus infinity is infinity 3. Infinity multiplied by bounded quantity is infinity
• 8. If the absolute value of P is less than 1, then the power of limp is n, where n is infinite and infinitesimal. Then why is this limit equal to 0
• 9. If the limit of function 1 / (x ^ 2) is positive infinity at x = 0, is there a limit at x = 0?
• 10. On the limit of function: the numerator is LNX, and the denominator is x ^ a (a > 0). The limit of this number can be obtained by variable substitution, and X tends to infinity
• 11. This is to use the relationship between limit and infinitesimal to find limit If LIM (x → 0) (sin6x + XF (x)) / x ^ 3 = O, then LIM (x → 0) (6 + F (x)) / x ^ 2 is But what I calculate is 0 for LIM (x → 0) (sin6x + XF (x)) / x ^ 3 = O. if the left side of the equation is divided by X, we will get LIM (x → 0) (6 + F (x)) / x ^ 2 = O. the error in solving the equation is
• 12. Can an infinitesimal number be multiplied by an infinitesimal number to get an infinitesimal number?
• 13. What is the result of infinitesimal multiplied by infinity? How to analyze this kind of problem?
• 14. Learn the limit to tell the infinitesimal times infinity is equal to how much, why?
• 15. Infinity - is infinity necessarily infinitesimal?
• 16. What are the properties of infinity and infinitesimal?
• 17. On infinitesimal and infinity Is the function y = xcosx bounded from negative infinity to positive infinity? Is this function infinitesimal when x approaches positive infinity? Why?
• 18. ---The problem of infinity and infinitesimal When X - > 0, is | x | / X infinite or infinitesimal? Please tell me why
• 19. Given that a > 1, the function f (x) = the third power of X - ax is a monotone increasing function on [1, + infinity), then the maximum value of a is?
• 20. Given that a > 0, f (x) = - X3 + ax is a monotone decreasing function in [1, + ∞), then the maximum value of a is () A. 1B. 2C. 3D. 4