Limx → 0sin3x / sin5x, find the limit

lim sin3x/sin5x
=lim 3x/(5x)
=3/5
＝＝＝＝＝＝＝＝
When x tends to zero, sin3x is equivalent to 3x, sin5x is equivalent to 5x

RELATED INFORMATIONS

1. Find the limit: limx (1 + 2x) &# 185; divide by the square of X, when x approaches 0, how to find it,
2. 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
3. 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
4. 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?
5. 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,
6. 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
7. Is infinitesimal divided by infinity or infinitesimal?
8. What is infinity multiplied by infinity? What is infinitesimal multiplied by infinitesimal? What is infinity plus infinitesimal?
9. How much is infinitesimal multiplied by infinity
10. If the solution set of inequality ax > b about X is (1, positive infinity), then the solution set of inequality (ax-b) / X-2 > 0 about X is (1, positive infinity) The answer is less than negative 1, greater than 2. Why is a greater than zero? If B is negative, it's OK
11. 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?
12. LIM (x approaches infinity) √ (the square of x-3x) / 2x + 1 How to do it
13. lim(x→1)(x^2-2x+1)/lnx-x+1
14. 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
15. Limit: when x tends to positive infinity, does the limit of function f (x) = LNX ax tend to negative infinity;
16. Find the limit of function (x / x-1) - (1 / LNX) x tending to 1
17. What is the power of infinitesimal to infinity? 0^∞ =0
18. What is infinity divided by infinitesimal
19. 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)
20. What is the infinite power of E?