### All AP Calculus BC Resources

## Example Questions

### Example Question #1 : Radius And Interval Of Convergence Of Power Series

Which of following intervals of convergence cannot exist?

**Possible Answers:**

For any , the interval for some

For any such that , the interval

**Correct answer:**

Explanation:

cannot be an interval of convergence because a theorem states that a radius has to be either nonzero and finite, or infinite (which would imply that it has interval of convergence ). Thus, can never be an interval of convergence.

### Example Question #1 : Radius And Interval Of Convergence Of Power Series

Find the interval of convergence of for the series .

**Possible Answers:**

**Correct answer:**

Explanation:

Using the root test,

Because 0 is always less than 1, the root test shows that the series converges for any value of x.

Therefore, the interval of convergence is:

### Example Question #2 : Taylor's Theorem

Find the interval of convergence for of the Taylor Series .

**Possible Answers:**

**Correct answer:**

Explanation:

Using the root test

and

. T

herefore, the series only converges when it is equal to zero.

This occurs when x=5.

Brandon

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Certified Tutor

University of Illinois at Urbana Champaign, Bachelor of Science, Mathematics.