Learn the limit to tell the infinitesimal times infinity is equal to how much, why?

RELATED INFORMATIONS

• 1. What is the result of infinitesimal multiplied by infinity? How to analyze this kind of problem?
• 2. Can an infinitesimal number be multiplied by an infinitesimal number to get an infinitesimal number?
• 3. 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
• 4. 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
• 5. 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
• 6. 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
• 7. 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
• 8. 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
• 9. Is limit equal to infinity the existence or non existence of limit?
• 10. Does limit infinity and infinitesimal exist
• 11. Infinity - is infinity necessarily infinitesimal?
• 12. What are the properties of infinity and infinitesimal?
• 13. 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?
• 14. ---The problem of infinity and infinitesimal When X - > 0, is | x | / X infinite or infinitesimal? Please tell me why
• 15. 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?
• 16. 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
• 17. Given that f (x) = X3 ax is a monotone increasing function on [1, + ∞), then the maximum value of a is______ ．
• 18. If the function f (x) is an odd function defined on R and a decreasing function on the interval (negative infinity, 0), and f (x) = 0, then f (x)
• 19. The function f (x) = x3-x is known to decrease on (0, a) and increase on [a, + ∞). The value of a is obtained. The expert is requested to answer
• 20. Find the circumference of a circle with radius or diameter. Find the area of a circle with radius or diameter