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 $\frac{\mathrm{\pi }}{4}$

Short answer

Ans:

Step-by-step solution

Step 1. Given information.

given,

Construct examples of given things

Step 2.