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Chapter 5: Q. 2 (page 494)

What it means for a rational function to be improper ?

Short Answer

Expert verified

A Rational function is improper when the degree of denominator function is less than or equal to degree of numerator function.

Step by step solution

01

Step 1. Defination

A Rational function $Q (x)$ which is ratio of two polynomial function localid="1651835937616" $P (x) and R (x)$ such that $Q (x) = \frac{P (x)}{R (x)}$ where $R (x) \neq 0$ is called improper if the degree of polynomial function of denominator i.e. $R (x)$ is less than the or equal to degree of the polynomial function in numerator i.e. $P (x)$

02

Step 2. Example

Example of rational function which is improper is $Q (x) = \frac{4 x^{4} + 7}{3 x - 1}$

Where $P (x) = 4 x^{4} + 7 and R (x) = 3 x - 1$ .

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Most popular questions from this chapter

Solve given definite integral.

$\int_{3}^{5} \sqrt{x^{2} - 9} d x$

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Solve given definite integral.

$\int_{0}^{4} x^{3} \sqrt{x^{2} + 4} d x$

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