### All AP Calculus BC Resources

## Example Questions

### Example Question #3 : Concepts Of Convergence And Divergence

Which of following intervals of convergence cannot exist?

**Possible Answers:**

For any such that , the interval

For any , the interval for some

**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 #1 : Taylor Series

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.

Ellis

Certified Tutor

Certified Tutor

Temple University, Bachelor of Science, Applied Physics. University of Wisconsin, Master of Science, Astrophysics.

Ping

Certified Tutor

Certified Tutor

The University of Texas at Dallas, Bachelor of Science, Computer Science. University of North Texas, Master of Arts, Education.

### All AP Calculus BC Resources

Popular Subjects

Algebra Tutors in Los Angeles, Computer Science Tutors in Denver, Math Tutors in Philadelphia, Spanish Tutors in Denver, Math Tutors in Chicago, LSAT Tutors in New York City, GRE Tutors in Denver, GRE Tutors in Washington DC, Math Tutors in Houston, Statistics Tutors in San Francisco-Bay Area
Popular Courses & Classes

ISEE Courses & Classes in Washington DC, Spanish Courses & Classes in Boston, ACT Courses & Classes in Phoenix, SSAT Courses & Classes in Philadelphia, MCAT Courses & Classes in San Francisco-Bay Area, GRE Courses & Classes in Denver, LSAT Courses & Classes in San Francisco-Bay Area, ISEE Courses & Classes in Boston, MCAT Courses & Classes in Phoenix, MCAT Courses & Classes in New York City
Popular Test Prep

GRE Test Prep in Washington DC, GMAT Test Prep in San Diego, SAT Test Prep in Seattle, ISEE Test Prep in Seattle, SAT Test Prep in Denver, SSAT Test Prep in New York City, ACT Test Prep in New York City, GRE Test Prep in New York City, ACT Test Prep in Houston, LSAT Test Prep in Los Angeles