Question

Find the limit limx→+[infinity]ex+e−xex−e−x limx→+[infinity]ex+e−xex−e−x Enter inf for [infinity] [infinity] , -inf for −[infinity] −[infinity] , and DNE if the limit does not exist. Answer: HINT: Factor ex ex out of the numerator and denominator

Answer 1

Answer:

1

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

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

Hence the limit of the given function is 1