Question

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.

Answer 1

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.