Question

Calculate the value of the limit to the indicated values of x then draw the graphf (x) = (x² -1 ) / (x-1,) with x = 1

Answer 1

Given:

The function is,

`\lim _(x\to1)((x^2-1))/((x-1))`

Take the limit as x tends to 1,

`\begin{gathered} \lim _(x\to1)((x^2-1))/((x-1)) \\ \text{Applying the limit as x=1 it will give }(0)/(0)\text{ form } \\ So,\text{ simplify the function.} \\ \lim _(x\to1)((x^2-1))/((x-1))=\lim _(x\to1)\frac{(x^{}-1)(x+1)}{(x-1)}=\lim _(x\to1)(x+1)=1+1=2 \end{gathered}`

The limit of the function is 2.

The graph of the function is,