Answer:
Step-by-step explanation:
We know the definition of both functions: 
, and 
A) In order to evaluate what 
, let's first investigate what g(-1) is using the definition for this function:
Now let's find what f(2) is using f(x) definition: 
B) In order to evaluate what 
, let's first investigate what f(3) is using the definition for this function:
Now let's find what g(7) is using the definition for this function:
Vol. of a rect. prism is V = L*W*H.
Here, that vol. is V = (2.5 ft)(1.5 ft)(4 ft) = 15 cubic feet (answer)
Note: volume (not valume).
Answer:
1-i and -1+i
Step-by-step explanation:
We are to find the square roots of 
. First, convert from Cartesian to polar form:
Next, use the formula ![\displaystyle \sqrt[n]{r}\biggr[\cis\biggr(\frac{\theta+2\pi k}{n}\biggr)\biggr]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Csqrt%5Bn%5D%7Br%7D%5Cbiggr%5B%5Ccis%5Cbiggr%28%5Cfrac%7B%5Ctheta%2B2%5Cpi%20k%7D%7Bn%7D%5Cbiggr%29%5Cbiggr%5D)
where 
to find the square roots:
<u>When k=1</u>
<u />![\displaystyle \sqrt[2]{2}\biggr[cis\biggr(\frac{\frac{3\pi}{2}+2\pi(1)}{2}\biggr)\biggr]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Csqrt%5B2%5D%7B2%7D%5Cbiggr%5Bcis%5Cbiggr%28%5Cfrac%7B%5Cfrac%7B3%5Cpi%7D%7B2%7D%2B2%5Cpi%281%29%7D%7B2%7D%5Cbiggr%29%5Cbiggr%5D)
![\displaystyle \sqrt{2}\biggr[cis\biggr(\frac{3\pi}{4}+\pi\biggr)\biggr]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Csqrt%7B2%7D%5Cbiggr%5Bcis%5Cbiggr%28%5Cfrac%7B3%5Cpi%7D%7B4%7D%2B%5Cpi%5Cbiggr%29%5Cbiggr%5D)
<u>When k=0</u>
<u />![\displaystyle \sqrt[2]{2}\biggr[cis\biggr(\frac{\frac{3\pi}{2}+2\pi(0)}{2}\biggr)\biggr]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Csqrt%5B2%5D%7B2%7D%5Cbiggr%5Bcis%5Cbiggr%28%5Cfrac%7B%5Cfrac%7B3%5Cpi%7D%7B2%7D%2B2%5Cpi%280%29%7D%7B2%7D%5Cbiggr%29%5Cbiggr%5D)
Thus, the square roots of -2i are 1-i and -1+i
Step-by-step explanation:
Limit as x approaches 5 from the left is 5^2 + 5(5) + 4 = 54
Limit as x approaches 5 from the right is -6(5)+3=-27
