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Xelga [282]
3 years ago
12

What is lim x → 0 e^2x - 1/ e^x - 1

Mathematics
1 answer:
olya-2409 [2.1K]3 years ago
4 0

Hello, please consider the following.

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

Thank you

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