Find the first 7 terms for the Taylor Series at 0 f(x)=11+x Make a substitution in the above taylore series to get the first 7 terms for the Taylor Series f(x)=11−x

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Find the first 7 terms for the Taylor Series at 0  f(x)=11+x  Make a substitution in the above taylore series to get the first 7 terms for the Taylor Series  f(x)=11−x

Cristiano Sears · Accepted Answer

Given,The function f(x)=11+x. We have to find the first seven terms for the Taylor series at 0. Also, make a substitution in the above Taylor series to get the first seven terms for the Taylor Series f(x)=11−xConcept UsedThe general term of Taylor&#039;s series of a function f(x) at x=a is f(x)=∑n=0∞fn(a)(x−a)nn!Calculation:f(x)=11+x⇒f(0)=11+0=1f′(x)=−12(1+x)32⇒f′(0)=−12(1+0)32=−12f″(x)=322(1+x)52⇒f″(0)=322(1+0)52=−322f‴(x)=−3×523(1+x)72⇒f‴(0)=−3×523(1+0)72=−1523f4(x)=−3×5×724(1+x)92⇒f4(0)=−3×5×724(1+0)92=10524f5(x)=−3×5×7×925(1+x)112⇒f5(0)=−3×5×7×925(1+0)112=−94525f6(x)=−3×5×7×9×1126(1+x)132⇒f6(0)=−3×5×7×9×1126(1+0)132=1039526f7(x)=−3×5×7×9×11×1327(1+x)152⇒f7(0)=−3×5×7×9×11×1327(1+0)152=−13513527Now, the first seen terms of Taylor&#039;s series for the functions f(x)=11+x at x=0 isf(x)=f(0)+f′(0)x+f″(0)x22!+f‴(0)x33!+f4(0)x44!+f5(0)x55!+f6(0)x66!+f7(0)x77!+...

Jeffrey Jordon · Accepted Answer

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Find the first 7 terms for the Taylor Series at 0 f(x)=frac{1}{sqrt{1+x}} Make a substitution in the above taylore series to get the first 7 terms for the Taylor Series f(x)=frac{1}{sqrt{1-x}}

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