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Chapter 8: Q. 23 (page 692)

In Exercises 23鈥�32 we ask you to give Lagrange鈥檚 form for the corresponding remainder, R4(x)

cosx

Short Answer

Expert verified

The required answer isR4(x)=-sinc120x5

Step by step solution

01

Step 1. Given Information

The given function isf(x)=cosx

02

Step 2. Explanation

Using the Lagrange form of remainder, we have,

Rn(x)=fn+1(c)(n+1)!xn+1R4(x)=f5(c)5!x5

Now, we will find fifth derivative of the function.

f1(x)=-sinxf2(x)=-cosxf3(x)=sinxf4(x)=cosxf5(x)=-sinx

Thus, we get,

R4(x)=-sinc120x5

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