Partial Fraction Decomposition on TI-89

This tutorial explains how to perform partial fraction decomposition using the TI-89 graphing calculator. It begins with an introduction to the concept and its relevance in calculus. The video then provides detailed instructions on setting up the calculator and demonstrates three examples of decomposition, each with step-by-step guidance. The tutorial concludes with helpful tips for using the TI-89 effectively.

What is the primary purpose of partial fraction decomposition in calculus?

• To solve linear equations

• To simplify complex fractions for easier integration

• To graph functions on a calculator

• To find the derivative of a function

Which menu option on the TI-89 is used to start a new problem?

• F6

• F3

• F2

• F1

What function is used on the TI-89 to perform partial fraction decomposition?

• Simplify

• Expand

• Factor

• Solve

In the first example, what is the denominator of the fraction to be decomposed?

• x squared plus x plus six

• x squared minus x minus six

• x minus three

• x plus two

What is the result of the partial fraction decomposition in the first example?

• 4/(x+2) + 6/(x-3)

• 10/(x-2) + 5/(x+3)

• 3/(x+1) + 7/(x-4)

• 2/(x+5) + 8/(x-6)

In the second example, what is the numerator of the fraction to be decomposed?

• 3x + 8

• 10x + 5

• 7x + 15

• 5x + 12

What is the first term in the decomposition of the second example?

• 43/(2(x-4))

• 29/(2x)

• 15/(x+3)

• 7/(x-1)

In the third example, what is unique about the denominator?

• It is in factored form

• It is a simple linear expression

• It contains a trigonometric function

• It is a constant

What is the second term in the decomposition of the third example?

• 7/(x-1)

• 5/(x-2)

• 13/(x-2)^2

• 3/(x+4)

What is the final term in the decomposition of the third example?

• 13/(x-2)^2

• 5/(x-2)

• 3/(x+4)

• 7/(x-1)