Answer:
256
Step-by-step explanation:
Raise 4 to the power of 4
Basically, multiply 4 by itself four times. :)
Answer:
a) Arithmetic yₙ = 3*(n - 1) + 13
b) Geometric yₙ = 2*5⁽ⁿ⁻¹⁾
Step-by-step explanation:
Answer:
0.5,1.2,23,-34,-73
Step-by-step explanation:
Answer:
The answer is
![f(x) = {\displaystyle 8 + \frac{-28}{1}(x+2)+\frac{-36}{2!}(x+2)^2 + \frac{-18}{3!}(x+2)^2 }](https://tex.z-dn.net/?f=f%28x%29%20%3D%20%7B%5Cdisplaystyle%20%208%20%2B%20%5Cfrac%7B-28%7D%7B1%7D%28x%2B2%29%2B%5Cfrac%7B-36%7D%7B2%21%7D%28x%2B2%29%5E2%20%2B%20%5Cfrac%7B-18%7D%7B3%21%7D%28x%2B2%29%5E2%20%7D)
Step-by-step explanation:
Remember that Taylor says that
![f(x) = {\displaystyle \sum\limits_{k=0}^{\infty} \frac{f^{(k)}(a) }{k!}(x-a)^k }](https://tex.z-dn.net/?f=f%28x%29%20%3D%20%7B%5Cdisplaystyle%20%5Csum%5Climits_%7Bk%3D0%7D%5E%7B%5Cinfty%7D%20%5Cfrac%7Bf%5E%7B%28k%29%7D%28a%29%20%7D%7Bk%21%7D%28x-a%29%5Ek%20%7D)
For this case
![f^{(0)} (-2) = 8(-2)-3(-2)^3 = 8\\f^{(1)} (-2) = 8-3(3)(-2)^2 = -28\\f^{(2)} (-2) = -3(3)2(-2) = -36\\f^{(2)} (-2) = -3(3)2 = -18](https://tex.z-dn.net/?f=f%5E%7B%280%29%7D%20%28-2%29%20%3D%208%28-2%29-3%28-2%29%5E3%20%3D%208%5C%5Cf%5E%7B%281%29%7D%20%28-2%29%20%3D%208-3%283%29%28-2%29%5E2%20%3D%20-28%5C%5Cf%5E%7B%282%29%7D%20%28-2%29%20%3D%20-3%283%292%28-2%29%20%3D%20-36%5C%5Cf%5E%7B%282%29%7D%20%28-2%29%20%3D%20-3%283%292%20%3D%20-18)
![f(x) = {\displaystyle 8 + \frac{-28}{1}(x+2)+\frac{-36}{2!}(x+2)^2 + \frac{-18}{3!}(x+2)^2 }](https://tex.z-dn.net/?f=f%28x%29%20%3D%20%7B%5Cdisplaystyle%20%208%20%2B%20%5Cfrac%7B-28%7D%7B1%7D%28x%2B2%29%2B%5Cfrac%7B-36%7D%7B2%21%7D%28x%2B2%29%5E2%20%2B%20%5Cfrac%7B-18%7D%7B3%21%7D%28x%2B2%29%5E2%20%7D)