Use the power series for $f ( x ) = \sqrt [ 3 ] { 5 + x }$ to estimate $\sqrt [ 3 ] { 5.07 }$ correct to four decimal places.
Select the correct answer.
A) $1.7179$
B) $1.7189$
C) $1.7195$
D) $1.7156$
E) $1.7200$

Question

Quizplus · Accepted Answer

The first four terms of the power series for $f ( x ) = \sqrt [ 3 ] { 5 + x }$ are$$1 + \frac { 1 } { 3 } x - \frac { 1 } { 9 } x ^ { 2 } + \frac { 5 } { 81 } x ^ { 3 } + \cdots$$So,$$\sqrt [ 3 ] { 5.07 } \approx 1 + \frac { 1 } { 3 } ( 0.07 ) - \frac { 1 } { 9 } ( 0.07 ) ^ { 2 } + \frac { 5 } { 81 } ( 0.07 ) ^ { 3 } = 1.7189$$

Use the Power Series For f(x)=5+x3f ( x ) = \sqrt [ 3 ] { 5 + x }f(x)=35+x​

Use the Power Series For $f ( x ) = \sqrt [ 3 ] { 5 + x }$