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bija089 [108]
3 years ago
7

Find the limit limx→+[infinity]ex+e−xex−e−x limx→+[infinity]ex+e−xex−e−x Enter inf for [infinity] [infinity] , -inf for −[infini

ty] −[infinity] , and DNE if the limit does not exist. Answer: HINT: Factor ex ex out of the numerator and denominator
Mathematics
1 answer:
Sergeeva-Olga [200]3 years ago
7 0

Answer:

<h3>1</h3>

Step-by-step explanation:

Given the expression:

\lim_{n \to \infty} \frac{e^x+e^{-x}}{e^x-e^{-x}}\\

factor out e^x from the numerator and denominator

\lim_{n \to \infty} \frac{e^x+e^{-x}}{e^x-e^{-x}}\\\lim_{n \to \infty} \frac{e^x(1+e^{-2x})}{e^x(1-e^{-2x})}\\\lim_{n \to \infty} \frac{(1+e^{-2x})}{(1-e^{-2x})}\\ =  \frac{(1+e^{-2(\infty)})}{(1-e^{-2(infty)})}\\= \frac{1+0}{1-0}\\= 1\\

<em>Hence the limit of the given function is 1</em>

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