The limit of function f (x) = | x | / X at x = 0 | Math enthusiast | Mathematical art

The limit of function f (x) = | x | / X at x = 0

The limit of F (x) is 1 when x tends to 0 from greater than 0
When x tends to zero from less than 0, the limit is - 1
Because the left limit is not equal to the right limit, f (x) is discontinuous at x = 0, so the limit does not exist

RELATED INFORMATIONS

1. What is the limit of the function f (x) = sgnx x → 0?
2. Let y = f (x) be a decreasing function defined on (0, positive infinity) and satisfy f (XY) = f (x) + F (y), f (1 / 3) = 1, (1) Find the value of F (1); (2) If there is a real number m such that f (m) = 2, find the value of M; (3) If f (x) + F (2-x)
3. Fixed value theorem of continuous function Let f (x) be continuous on a closed interval [1,3] (1) If f (1) + F (2) + F (3) = 3, try to prove that there is at least one point a on [1,3] so that f (a) = 1
4. Who can help me prove the boundedness of function and the maximum and minimum theorem The property theorem of continuous function on closed interval: the continuous function on closed interval is bounded on the interval, and it must be able to obtain its maximum and minimum value. This theorem is easy to understand with graph, I hope someone can prove it with mathematical language,
5. Bolzano Weierstrass theorem. Does this theorem have a Chinese name?
6. If the spring can change suddenly, it means that there is displacement in the limit time, X / T = V (time limit), and the pushing speed is infinite (but the speed cannot be infinite) But if one end of the spring is not connected with a mass object, the deformation of the light spring does not need time, can the elastic force change suddenly?
7. It is proved that the limit of 2 ^ (1 / x) when x tends to 0 - is 0?
8. It is proved that the value of X (x + 1) (x + 2) (x + 3) + 1 is a complete square expression Try to be quick
9. The function f (x) is defined at x = 1. What is the condition for the existence of LIM (x tends to 1) f (x)? Just say that it is sufficient or necessary, or it is neither sufficient nor necessary,
10. Given the vector a = (2cosx, 1), B = (cosx, root 3sin2x-1), Let f (x) = vector a * vector B, where x ∈ R (1) find the minimum positive period of the function And monotone increasing interval
11. If the function f (x) has a limit at X., then f (x) is at x = X A may not define B continuous C differentiable D discontinuous
12. The limit of function f (x) = 2 ^ (1 / x) at x = 0 Explain the left and right limits
13. Does the function f (x) = (- 1) ^ X have a limit
14. The function f (x) = (1-x) (x-3) is transformed into vertex form The answer is to change f (x) = (1-x) (x-3) into the vertex form and then (x-1) ^ 2 - 4 I've been working out - (X-2) ^ 2 + 1 for a long time. I don't know how to work out the answer
15. The function f (x) = 1 / x, when x →∞, the limit of F (x) is 0, so according to the limit must converge, the function should be convergent and bounded, but real
16. What is the limit of function f (x) = 1 Does it have limits? Yes, come on, I don't know calculus
17. How to prove the limit of X multiplied by sin1 / x? I can't understand it. I hope you can give me some advice It is proved by definition that x tends to 0 - and the limit value is 0
18. Why is the limit of x times sin1 / X not one
19. ((x + 1) ^ (x + 1) / x ^ x) * sin1 / x x tends to infinity to find limit
20. When x tends to infinity, why is it wrong that the limit of xsin1 / x = the limit of X multiplied by the limit of sin1 / x = 0