Answer:
See Below.
Step-by-step explanation:
We want to show that the function:

Increases for all values of <em>x</em>.
A function is increasing whenever its derivative is positive.
So, find the derivative of our function:
![\displaystyle f'(x) = \frac{d}{dx}\left[e^x - e^{-x}\right]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20f%27%28x%29%20%3D%20%5Cfrac%7Bd%7D%7Bdx%7D%5Cleft%5Be%5Ex%20-%20e%5E%7B-x%7D%5Cright%5D)
Differentiate:

Simplify:

Since eˣ is always greater than zero and e⁻ˣ is also always greater than zero, f'(x) is always positive. Hence, the original function increases for all values of <em>x.</em>
Answer:
34%
Step-by-step explanation:
To find what percent a part is of the whole, divide the part by the whole and multiply by 100%.

Answer:
Answer:
164.32 earth year
Step-by-step explanation:
distance of Neptune, Rn = 4.5 x 10^9 km
distance of earth, Re = 1.5 x 10^8 km
time period of earth, Te = 1 year
let the time period of Neptune is Tn.
According to the Kepler's third law
T² ∝ R³


Tn = 164.32 earth years
Thus, the neptune year is equal to 164.32 earth year.
Step-by-step explanation:
Given two points (X1,Y1) and (X2,Y2) on a line, the slope =(Y2 - Y1) /(X2 - X1).
You are given the points (1,3) and (3,-2). Implying X1 =1 , Y1 =3, X2=3, Y2=-2
Use the formula for the slope above to answer the question. If you still have problems getting the correct answer, ask for more help.
Your answer should be a negative fraction or decimal if you are using a calculator.