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.

a. lim(x→∞) tanh x

Accepted Answer

Welcome back, everyone. Evaluate the limit using the definition of 1 X. Limit as X approaches negative infinity of tinge of X divided by 2. For this problem, let's remember what tinge is. We can express tinge X as the power of X minus E to the power of negative X. Divided by the power of X plus e to the power of negative X. Now, in this case, we have a different angle and that would be tinge of X divided by 2, right? So, we're going to take E to the power of X divided by 2 minus E to the power of negative X divided by 2. Divided by e to the power of X divided by 2 plus e to the power of negative X divided by 2. And to simplify the analysis, we're going to divide all of our terms by E to the power of negative X divided by 2. So we can also express change of X divided by 2 is to the power of X minus 1. Divided by It's the power of X + 1. Therefore, if we want to take the limit, we can basically take the limit as X approaches negative infinity of E to the power of X minus 1. Divided by the power of X + 1. And then we can use direct substitution. Each the power of X as X approaches infinity represents an exponential decay to zero, right? Because our exponent is Infinitely negative. So whenever we erase each the power of negative infinity, this approach is 0. We get 0 minus 1 in the numerator, and 0 + 1 in the denominator. So that 1 divided by 1 gives us a limit of -1, and the answer is -1. Thank you for watching.

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

Watch next

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