Answer:
Integral will be diverging in nature
Step-by-step explanation:
We have given integral 
Now after solving the integral
limit from 5 to infinite
So ![[\frac{3}{2}\frac{\infty^3}{3}]-[\frac{3}{2}\times \frac{5^3}{3}]=\infty](https://tex.z-dn.net/?f=%5B%5Cfrac%7B3%7D%7B2%7D%5Cfrac%7B%5Cinfty%5E3%7D%7B3%7D%5D-%5B%5Cfrac%7B3%7D%7B2%7D%5Ctimes%20%5Cfrac%7B5%5E3%7D%7B3%7D%5D%3D%5Cinfty)
As after solving integral we got infinite value so integral will be diverging in nature
To find the inverse, we swap the variables y and x, then solve for the new y.
3a.

Swapping the variables:

Solving for y:

The domain of this inverse is

.
3b.

Swapping:

Solving for y:

The domain of this inverse is

.
3c.
![y=\sqrt[3]{\frac{x-7}{3}}](https://tex.z-dn.net/?f=y%3D%5Csqrt%5B3%5D%7B%5Cfrac%7Bx-7%7D%7B3%7D%7D)
Swapping:
![x=\sqrt[3]{\frac{y-7}{3}}](https://tex.z-dn.net/?f=x%3D%5Csqrt%5B3%5D%7B%5Cfrac%7By-7%7D%7B3%7D%7D)
Solving for y:

The domain of this inverse is all real numbers.
4a.

,


4c.
![y=\sqrt[3]{\frac{x-7}{3}}](https://tex.z-dn.net/?f=y%3D%5Csqrt%5B3%5D%7B%5Cfrac%7Bx-7%7D%7B3%7D%7D)
,

![y=\sqrt[3]{\frac{(3x^3+7)-7}{3}} \\ y=\sqrt[3]{\frac{3x^3}{3}} \\ y=\sqrt[3]{x^3} \\ y=x](https://tex.z-dn.net/?f=y%3D%5Csqrt%5B3%5D%7B%5Cfrac%7B%283x%5E3%2B7%29-7%7D%7B3%7D%7D%20%5C%5C%20y%3D%5Csqrt%5B3%5D%7B%5Cfrac%7B3x%5E3%7D%7B3%7D%7D%20%5C%5C%20y%3D%5Csqrt%5B3%5D%7Bx%5E3%7D%20%5C%5C%20y%3Dx)
Answer:
The value of car after 14 years is $ 2,363.04
Step-by-step explanation:
Given as :
The price of new car = N = $ 18,000
The rate of depreciation of the value of the car = R = 13.5 % per year
Let The value of car after 14 years = $ x
The time period = 14 years
<u>Now, According to question</u>
The value of car after n years = initial value of car × 
or, $ x = N × 
or, $ x = $ 18,000 × 
Or, $ x = $ 18,000 × 
∴ x = $ 18,000 × 0.13128
I.e x = $ 2,363.04
So, The value of car after 14 years = x = $ 2,363.04
Hence The value of car after 14 years is $ 2,363.04 Answer
It would be false
*Character limit fill ignore*