Question

lim e^2x-1/e^x-1 as x approaches 0

Answer 1

\[\lim_{x \rightarrow 0} e ^{2x}-1\div e ^{x}-1\]

Answer 2

factor out the numerator,
e^2x - 1 = (e^x)^2 - 1 = (e^x + 1)(e^x - 1)

then cancel's the similar in the numerator and the denominator
now we have :
lim x->0 (e^x + 1) = e^0 + 1 = 1 + 1 = 2