### All High School Math Resources

## Example Questions

### Example Question #1 : Understanding Taylor Series

Give the term of the Maclaurin series of the function

**Possible Answers:**

**Correct answer:**

The term of the Maclaurin series of a function has coefficient

The second derivative of can be found as follows:

The coeficient of in the Maclaurin series is therefore

### Example Question #2 : Understanding Taylor Series

Give the term of the Taylor series expansion of the function about .

**Possible Answers:**

**Correct answer:**

The term of a Taylor series expansion about is

.

We can find by differentiating twice in succession:

so the term is

### Example Question #1 : Taylor And Maclaurin Series

Give the term of the Maclaurin series expansion of the function .

**Possible Answers:**

**Correct answer:**

This can most easily be answered by recalling that the Maclaurin series for is

Multiply by to get:

The term is therefore .

### Example Question #2 : Understanding Maclaurin Series

Give the term of the Maclaurin series of the function .

**Possible Answers:**

**Correct answer:**

The term of a Maclaurin series expansion has coefficient

.

We can find by differentiating three times in succession:

The term we want is therefore

### Example Question #1 : Applying Taylor Series

Give the term of the Maclaurin series expansion of the function .

**Possible Answers:**

**Correct answer:**

The term of a Maclaurin series expansion has coefficient

.

We can find by differentiating twice in succession:

The coefficient we want is

,

so the corresponding term is .

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