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Chapter 8: Q. 25 (page 692)

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

sinx

Short Answer

Expert verified

The required answer isR4(x)=cosc120x5

Step by step solution

01

Step 1. Given Information  

The given function isf(x)=sinx

02

Step 2. Explanation 

Using the Lagrange form for the remainder, we have,

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

Now, we will find the fifth derivative of the function as follows,

f1(x)=cosxf2(x)=-sinxf3(x)=-cosxf4(x)=sinxf5(x)=cosx

Thus, we get,

R4(x)=cosc5!x5R4(x)=cosc120x5

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