159k views
5 votes
Create or find your own, unique function h(x). discuss the limit of your function as latex: x x approaches some particular value, let's say a, where the limit exists but the y-value does not or is different than the limit.

1 Answer

3 votes
Consider the function:


h(x)= (x^2-1)/(x-1)

As x tends to 1,


h(1)= (1^2-1)/(1-1) = (0)/(0)

hence, the y value does not exist.

But


\lim_(x\to1) h(x)= \lim_(x\to1) (x^2-1)/(x-1) \\ \\ = \lim_(x\to1) ((x-1)(x+1))/(x-1)= \lim_(x\to1) (x+1) \\ \\ =1+1=2

Therefore, the limit of h(x) exists but the y-value does not exist.
User Black Beard
by
8.1k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories