How do you use linear approximation to estimate $\sqrt[3]{64.1}$ $root3( 64.1)$ ?

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Answer 1 · 2016-07-20T08:01:08

$\sqrt[3]{64.1} = 4.002083$ $root(3)64.1=4.002083$ .

For a fun. $f, f(x+h)~=f(x)+hf'(x).................(1)$ .

Consider the fun. $f(x)=root(3)x=x^(1/3) rArr f'(x)=1/3*x^(-2/3)$

We take $x=64, and, h=0.1$ in $(1)$ . Therefore,

$f(64+0.1)~=f(64)+0.1f'(64)$

$:.(64.1)^(1/3)~=64^(1/3)+0.1*1/3*64^(-2/3)=4+0.1*1/3*4^(-2)$

$=4+1/10*1/3*1/16=4+1/480~=4+0.002083=4.002083$ .

Thus, $root(3)64.1=4.002083$ .

How do you use linear approximation to estimate root3( 64.1)3√64.1root3( 64.1)?