Find the linear approximation of the function g(x) = 3 root 1 + x at a = 0. g(x). Use it to approximate the numbers 3 root 0.95
and 3 root 1.1.
1 answer:
Answer:

![\sqrt[3]{0.95} \approx 0.9833](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B0.95%7D%20%5Capprox%200.9833)
![\sqrt[3]{1.1} \approx 1.0333](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B1.1%7D%20%5Capprox%201.0333)
Step-by-step explanation:
Given the function: ![g(x)=\sqrt[3]{1+x}](https://tex.z-dn.net/?f=g%28x%29%3D%5Csqrt%5B3%5D%7B1%2Bx%7D)
We are to determine the linear approximation of the function g(x) at a = 0.
Linear Approximating Polynomial,
a=0
![g(0)=\sqrt[3]{1+0}=1](https://tex.z-dn.net/?f=g%280%29%3D%5Csqrt%5B3%5D%7B1%2B0%7D%3D1)

Therefore:

(b)![\sqrt[3]{0.95}= \sqrt[3]{1-0.05}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B0.95%7D%3D%20%5Csqrt%5B3%5D%7B1-0.05%7D)
When x = - 0.05

![\sqrt[3]{0.95} \approx 0.9833](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B0.95%7D%20%5Capprox%200.9833)
(c)
(b)![\sqrt[3]{1.1}= \sqrt[3]{1+0.1}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B1.1%7D%3D%20%5Csqrt%5B3%5D%7B1%2B0.1%7D)
When x = 0.1

![\sqrt[3]{1.1} \approx 1.0333](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B1.1%7D%20%5Capprox%201.0333)
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