limx → 0 (ax-1 / √ 1+x-1) is equal to

Question

limx → 0 (ax-1 / √ 1+x-1) is equal to (A) 2 log e a (B)  (1 /2) log e a (C) a log e 2 (D) none of these

Tardigrade Admin · Accepted Answer

limx→0 (ax - 1/√1 +x -1) = limx→0 (ax -1/√1 +x -1). (√1+x +1/√1+x +1) = limx→0 (ax -1/x) .(√1+x +1) = 2( logea)

Q. $lim_{x \to 0} \frac{a ^{x} - 1}{1 + x - 1}$ is equal to