Find the Taylor polynomial of degree n approximating the given function for x near 0.
sqrt(1+x)

How do I solve these sorts of problems

Question

Find the Taylor polynomial of degree n approximating the given function for  x near 0.
sqrt(1+x)

How do I solve these sorts of problems

ganeshie8 · Answer

taylor series at x = 0 gives u maclaurin series

ganeshie8 · Answer

$\large    f(x) =  f(0) +   xf'(0)  +   \frac{x^2}{2!}f''(0) +   \frac{x^3}{3!}f'''(0) + ....$

ganeshie8 · Answer

start by finding first "n" derivatives of given function and plug them above

ganeshie8 · Answer

$\large  f(x) =  \sqrt{1+x}$

$\large  f(0) =  ?$

$\large  f'(0) =  ?$

$\large  f''(0) =  ?$

$\large  f'''(0) =  ?$

anonymous · Answer

ohh okay, so 1/2
-1/4
3/8
and so forth. thanks! :)

ganeshie8 · Answer

yes, divide them by factorial terms also
that gives coefficients of polynomial

ganeshie8 · Answer