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Question

Let $g\left(x ight)=\begin{cases}\frac{x^3-1}{x-1} & ext{if }x e1\ a & ext{if }x=1\end{cases}$

For what value of $a$ is $g (x)$ continuous at $x equals 1$ ?

Accepted Answer

Answer

Answer

Answer

Let g(x)={x3−1x−1if x≠1aif x=1g\left(x\right)=\begin{cases}\frac{x^3-1}{x-1} & \text{if }x\ne1\\ a & \text{if }x=1\end{cases}g(x)={x−1x3−1aif x=1if x=1For what value of aa is g(x)g\left(x\right) continuous at x=1x=1?