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.

c. lim(x→∞) sinh x

Accepted Answer

Welcome back, everyone. Evaluate the limit algebraically. Limit as X approaches negative infinity of sin of 4 X. A negative infinity B positive infinity, C 0, and D1. For this problem, let's rewrite the limits. Limit as X approaches negative infinity of singe of 4 X. Let's use the definition of singe. We can express it in terms of E. And we are going to get E raise to the power of 4 X minus E raise the power of -4 X divided by 2. Let's go ahead and factor out the constant that would be 1/2. Multiplied by limit as x approaches negative infinity. And we have e to the power of 4 x minus. Or the negative exponent, we can turn it into a positive exponent if we use the reciprocal rule. So we can subtract one divided by E to the power of 4 X. And now let's analyze what's happening when X approaches negative infinity, right? We got 1/2 multiplied by. Let's add brackets to show that we're attempting to calculate, so we get E raise to the power of 4 multiplied by negative infinity gives us negative infinity, and we are subtracting 1 divided by E raise to the power of 4 multiplied by negative infinity. Once again that's negative infinity. So now, once again, we can apply the reciprocal rule to clearly understand what we have. The first term is going to become one divided by Eats the power of positive infinity. And for the second term, while we are subtracting. E To the power of positive infinity according to the reciprocal rule. Now it's the power of infinity is infinity, and when we divide one by an infinitely large number, we're going to get a limit of 0, and we are subtracting each to the power of infinity which is infinity, right? So overall, we get 1/2 multiplied by 0 minus infinity, gives us negative infinity. We can visualize it as negative infinity divided by 2. Which is basically negative infinity. Well then, so this is how we have got our limits. The answer to this problem corresponds to the answer choice A. Thank you for watching.

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

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