Answer:

Step-by-step explanation:
We are to determine the limit below.

Plug in 8 into the function.

The reducing factor is 1/5. The rectangular rug 12.5 feet long and 10 feet wide needs to be reduced by a factor of 1/5.
The area of the reduced rug will be the new long times the new wide.
New long = 12.5 feet * 1/5 = 2.5 feet
New wide = 10 feet * 1/5 = 2.0 feet
New area = 2.5 feet * 2.0 feet = 5.0 feet^2.
Answer: 5.0 ft^2
Answer:
The solution is ![\frac{1}{10} * tan^{-1}[\frac{e^{2x}}{5} ] + C](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B10%7D%20%2A%20tan%5E%7B-1%7D%5B%5Cfrac%7Be%5E%7B2x%7D%7D%7B5%7D%20%5D%20%2B%20%20C)
Step-by-step explanation:
From the question
The function given is 
The indefinite integral is mathematically represented as

Now let 
=> 
=> 
So

![= \frac{1}{2} \frac{tan^{-1} [\frac{u}{5} ]}{5} + C](https://tex.z-dn.net/?f=%3D%20%5Cfrac%7B1%7D%7B2%7D%20%5Cfrac%7Btan%5E%7B-1%7D%20%5B%5Cfrac%7Bu%7D%7B5%7D%20%5D%7D%7B5%7D%20%20%2B%20%20C)
Now substituting for u
![\frac{1}{10} * tan^{-1}[\frac{e^{2x}}{5} ] + C](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B10%7D%20%2A%20tan%5E%7B-1%7D%5B%5Cfrac%7Be%5E%7B2x%7D%7D%7B5%7D%20%5D%20%2B%20%20C)
Answer:
the answer is 19.06396
Step-by-step explanation:
there is no need for further explanation because the equation is already balanced