Taylor series Write out the first three nonzero terms of the Taylor series for the following functions centered at the given point a. Then write the series using summation notation. f(x)=cosh(2x-2),a=1

rocedwrp

rocedwrp

Answered question

2020-12-29

Taylor series Write out the first three nonzero terms of the Taylor series for the following functions centered at the given point a. Then write the series using summation notation.
f(x)=cosh(2x2),a=1

Answer & Explanation

sovienesY

sovienesY

Skilled2020-12-30Added 89 answers

We have to write first three nonzero terms of the taylor series for the function
f(x)=cosh(2x2),a=1
f(x)=cosh(2x2),f(1)=cosh(0)=1
f(x)=2sinh(2x2),f(1)=2sinh(0)=0
f(x)=4cosh(2x2),f(1)=4cosh(0)=4
f(x)=8sinh(2x2),f(1)=8sinh(0)=0
f4(x)=16cosh(2x2),f4(1)=16cosh(0)=16
f5(x)=32sinh(2x2),f5(1)=32sinh(0)=32
f6(x)=64cosh(2x2),f6(1)=64cosh(0)=64
First term f(1)=1
Second term f(1)(x1)=0,(x1)=0
Third term f(1)2!(x1)2=42!(x1)2=2(x1)2
Third term f(1)3!(x1)3=03!(x1)3=0
Fourth term f4(1)4!(x1)4=164!(x1)4=23(x1)4
Fifth term

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