Q. 2 - Calculus

Question

Construct examples of the thing(s) described in the following. Try to find examples that are different than any in the reading. 

(a) The third remainder $R_3\left(x\right)$ for sin x when $P_3\left(x\right)$ is the third Taylor polynomial for sin x at $\frac{\mathrm{\pi }}{4}$. 

(b) The integral given by Taylor’s Theorem is equal to the third remainder $R_3\left(x\right)$ for sin x when $P_3\left(x\right)$ is the third Taylor polynomial for sin x at $\frac{\mathrm{\pi }}{4}$ . 

(c) Lagrange’s form for the third remainder $R_3\left(x\right)$ for sin x when $P_3\left(x\right)$ is the third Taylor polynomial for sin x at $\frac{\mathrm{\pi }}{4}$

Step-by-Step Solution

Answer

Ans:  

Step 1. Given information.

given,

       Construct examples of given things

Step 2.