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

1

Explanation:

Given the expression:

`\lim_(n \to \infty) (e^x+e^(-x))/(e^x-e^(-x))\\`

factor out e^x from the numerator and denominator

`\lim_(n \to \infty) (e^x+e^(-x))/(e^x-e^(-x))\\\lim_(n \to \infty) (e^x(1+e^(-2x)))/(e^x(1-e^(-2x)))\\\lim_(n \to \infty) ((1+e^(-2x)))/((1-e^(-2x)))\\ = ((1+e^(-2(\infty))))/((1-e^(-2(infty))))\\= (1+0)/(1-0)\\= 1\\`

Hence the limit of the given function is 1