# Worksheet: Taylor Polynomials Approximation to a Function

In this worksheet, we will practice finding Taylor/Maclaurin polynomials and using them to approximate a function.

**Q1: **

Find the Taylor polynomials of the third degree approximating the function at the point .

- A
- B
- C
- D
- E

**Q2: **

Find the Taylor polynomials of the fourth degree approximating the function at the point .

- A
- B
- C
- D
- E

**Q3: **

Find the Taylor polynomials of the third degree approximating the function at the point .

- A
- B
- C
- D
- E

**Q4: **

Find the Taylor polynomials of the fourth degree approximating the function at the point .

- A
- B
- C
- D
- E

**Q5: **

Find the Taylor polynomials of degree two approximating the function at the point .

- A
- B
- C
- D
- E

**Q6: **

The tangent line gives a linear approximation to a function near a point. We consider higher order polynomials.

Suppose is twice differentiable at . Let be the polynomial satisfying , , and . In terms of , what are the coefficients , , and ?

- A
- B
- C
- D
- E

Is always a quadratic polynomial? Why?

- A yes, because we have coefficients up to degree 2
- B no, because the point may be an inflection point of

What is when at ? Give your coefficients as fractions.

- A
- B
- C
- D
- E

Using the function at , find the tangent line approximation of the cube root of 7 to 5 decimal places.

Using the function at , determine the quadratic approximation of the cube root of 7 to 5 decimal places.

**Q7: **

Find the third-degree Taylor polynomial of the function at the point .

- A
- B
- C
- D
- E

**Q8: **

Use the second-degree Taylor polynomial to approximate the function at the point .

- A
- B
- C
- D
- E

**Q9: **

Find the third-degree Taylor polynomial of the function at the point .

- A
- B
- C
- D
- E

**Q10: **

Find the fourth-degree Taylor polynomial of the function at the point .

- A
- B
- C
- D
- E