Question

What is lim x → 0 e^2x - 1/ e^x - 1

Answer 1

Hello, please consider the following.

`\displaystyle \forall x \in \mathbb{R}\\\\(e^(2x)-1)/(e^x-1)\\\\=((e^x)^2-1^2)/(e^x-1)\\\\=((e^x-1)(e^x+1))/(e^x-1)\\\\=e^x+1\\\\\text{So, we can find the limit.}\\\\\lim_(x\rightarrow 0) \ {(e^(2x)-1)/(e^x-1)}\\\\=\lim_(x\rightarrow 0) \ {e^x+1}\\\\=e^0+1\\\\\large \boxed{\sf \bf \ =2 \ }`

Thank you