Answer to Question #315437 in Complex Analysis for Roshan

Question #315437

obtain first three terms of taylors series for f(z) = sin z about 2=0


1
Expert's answer
2022-03-23T18:11:05-0400

"f\\left( 0 \\right) =\\sin 0=0\\\\f'\\left( 0 \\right) =\\cos z|_{z=0}=1\\\\f''\\left( 0 \\right) =-\\sin z|_{z=0}=0\\\\f'''\\left( 0 \\right) =-\\cos z|_{z=0}=-1\\\\f'^v\\left( 0 \\right) =\\sin z|_{z=0}=0\\\\f^v\\left( 0 \\right) =\\cos z|_{z=0}=1\\\\First\\,\\,3terms:\\\\f\\left( z \\right) =\\sum_{n=0}^5{\\frac{1}{n!}f^{\\left( n \\right)}\\left( z \\right) z^n}+o\\left( z^5 \\right) =z-\\frac{1}{3!}z^3+\\frac{1}{5!}z^5+o\\left( z^5 \\right) =\\\\=z-\\frac{1}{6}z^3+\\frac{1}{120}z^5+o\\left( z^5 \\right)"


Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!

Leave a comment

LATEST TUTORIALS
New on Blog
APPROVED BY CLIENTS