Evaluating hyperbolic functions Evaluate each expression witho...

Question

Evaluating hyperbolic functions Evaluate each expression without using a calculator or state that the value does not exist. Simplify answers as much as possible.

f. sinh (2 ln 3)

Accepted Answer

Welcome back, everyone. Evaluate sin of 2 LN of 2 without using a calculator. Simplify your answer as much as possible. A 15 divided by 8. B 17 divided by 5. C 8 divided by 15, and D 17 divided by 8. For this problem, let's recall the definition of sci of X, which is e raises the power of x minus E raises the power of negative X divided by 2. We can also write it as E raises the power of X minus 1 divided by E erase the power of X, all divided by 2, right, to essentially get rid of the negative sign for our exponent using the reciprocal rule. Using this formula, we can show that sin of 2 LN of 2 is then going to be equal toe raises the power of 2 LN of 2 minus 1 divided by E raises the power of 2 LN of 2 all divided by 2. What we want to do is now focus on E, raise the power of 2 LN of 2. We can use the properties of logarithms and specifically E raise the power of LN of A is going to be A, right? The problem, however, is that we have 2 in front of the log, so we can use another property. According to the reverse power rule for logarithms, we can say that LN of a raises the power of X X multiplied by LN of A, we can bring down the exponent. So if we go in reverse and if we have X in front of LN, we can basically Bring it on a and turn it into an exponent, right, so now we can get rid of that coefficient in front of the lock. So E raises the power of 2 of 2 can be written as E raises the power of LN of 2 squad. Which is he raised the power of Llan of 4. And now we're using the first property, this is equal to 4 because we have Ease the power of LN of 4, which is going to be 4. So now considering our expression for cinch we get. 4 minus 1 divided by 4 divided by 2. We can find the common denominator, which is 44 multiplied by 4 is 16, and 16 minus 1 is 15, so we got 15. Divided by 4 and then divided by 2. Which is equal to 15 divided by 4. Multiplied by 2, that's 15 divided by 8. So the correct answer for this problem is a. Thank you for watching.

Evaluating hyperbolic functions Evaluate each expression without using a calculator or state that the value does not exist. Simplify answers as much as possible.f. sinh (2 ln 3)

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Evaluating hyperbolic functions Evaluate each expression without using a calculator or state that the value does not exist. Simplify answers as much as possible.
f. sinh (2 ln 3)