49.0k views
3 votes
Find the limit of the function by using direct substitution.

limit as x approaches quantity pi divided by two of quantity three times e to the x times cosine of x.
The choices are:
a. 1
b. pi/2
c. 0
d. 5e^(pi/2)

User Rich Jones
by
7.9k points

1 Answer

4 votes

Answer:

Option a.


\lim_{x \to (\pi)/(2)}(3e)^(xcosx)=1

Explanation:

You have the following limit:


\lim_{x \to (\pi)/(2){(3e)^(xcosx)

The method of direct substitution consists of substituting the value of
(\pi)/(2) in the function and simplifying the expression obtained.

We then use this method to solve the limit by doing
x=(\pi)/(2)

Therefore:


\lim_{x \to (\pi)/(2)}{(3e)^(xcosx) = \lim_{x\to (\pi)/(2)}{(3e)^{(\pi)/(2)cos((\pi)/(2))}


cos((\pi)/(2))=0\\

By definition, any number raised to exponent 0 is equal to 1

So


\lim_{x\to (\pi)/(2)}{(3e)^{(\pi)/(2)cos((\pi)/(2))} = \lim_{x\to (\pi)/(2)}{(3e)^{(\pi)/(2)(0)}\\\\


\lim_{x\to (\pi)/(2)}{(3e)^(0)} = 1

Finally


\lim_{x \to (\pi)/(2)}(3e)^(xcosx)=1

User Jamesamuir
by
8.7k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories