82. Use the definitions of the hyperbolic functions to find ea...

Question

82. Use the definitions of the hyperbolic functions to find each of the following limits.

f. lim(x→∞) coth x

Accepted Answer

Welcome back, everyone. Compute the limit as x approaches negative infinity of c of X. A says 0 B 1 C1 and D infinity. For this problem before we begin with the calculation of the limit, let's remember the definition of the hyperbolic cotangent of X. If we divide cash by cich, we're going to get an expression of e to the power of X plus e to the power of negative x divided by Es the power of X minus e to the power of negative X. We can divide the numerator and the denominator by e to the power of negative X to get E to the power of 2 X plus 1. Divided by e to the power of 2 x minus 1. So we can use this expression in the calculation of the limit. Limit as X approaches negative infinity of E to the power of 2 X + 1 divided by e to the power of 2X minus 1. Now as x approaches negative infinity, e to the power of 2 X is going to approach. Eats the power of negative infinity. Well, that would be zero, right. Therefore, we can immediately calculate the limit as follows. If E to the power of 2 X approaches 0 as X approaches negative infinity, we get 0 + 1 in the numerator. And the 0 minus 1 and the denominator. Which leaves us with 1 divided by -1 and that's -1. So the answer to this problem corresponds to the answer choice B. Thank you for watching.

82. Use the definitions of the hyperbolic functions to find each of the following limits.f. lim(x→∞) coth x

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82. Use the definitions of the hyperbolic functions to find each of the following limits.
f. lim(x→∞) coth x