Let be the function g(x)= cases x^ 2 -1 x-1 , & x<1

MATHEMATICS · Subjective · AP · Calculus AB · Limits and Continuity · Limits and Continuity

Problem

Let gg be the function g(x)={x2−1x−1,x<1,ax+1,x≥1.g(x)= \begin{cases} \dfrac{x^{2}-1}{x-1}, & x<1,\\ a x+1, & x\ge 1. \end{cases} Determine the value of aa that guarantees lim⁡x→1g(x)\displaystyle\lim_{x\to 1} g(x) exists.

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