Question

Given () = ^3 + 8^2 + 15 − 24, find ( 11/10) by using Taylor′s theorem.

THIS WAS THE QUESTION..​

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Answer:

$f(\frac{11}{10} )=3.511$

Step-by-step explanation:

The correct question is:  Given that $f(x)=x^{3}+8x^{2}+15x-24$, find $f(11/10)$ using Taylor's theorem.

We know that $f(x)=x^{3}+8x^{2}+15x-24$

By Taylor's series, $f(x+h)=f(x)+hf^{'} (x)+\frac{h^2}{2!} f^{''} (x)+\frac{h^3}{3!} f^{'''} (x)+...$

Taking $x=1$ and $h=\frac{1}{10}=0.1$,

$f^'}(x)=3x^{2}+16x+15$

$f^''}(x)=6x+16$

$f^'''}(x)=6x$

$f^''''}(x)=0$

$\therefore$   $f(\frac{11}{10} )=f(1)+0.1f^{'}(1)+\frac{0.01}{2!} f^{''}(1)+.....$

              $=0+3.4+0.11+0.001$

              $=3.511$

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