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Chapter 1: Q. 90 (page 137)

Use limit rules and the continuity of polynomial functions to prove that every rational function is continuous on its domain.

Short Answer

Expert verified

A rational function r=pqis continuous at every point where q≠0.

Step by step solution

01

Step 1. Given Information:

Using limit rules and the continuity of power functions.

02

Step 2. Prove:

Consider any constant function,

f(x)=1

Again, the identity function g(x)=xare continuous on ℝ

03

Step 3. Every rational function is continuous in its domain 

Now scalar multiples, sums, and products imply that every polynomial is continuous onℝ

It also follows that a rational function r=pqis continuous at every point whereq≠0 .

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Most popular questions from this chapter

For each limit statement in Exercises 41-44, use algebra to find δor Nin terms of εor M, according to the appropriate formal limit definition.

limx→∞x2+2=∞,findNin terms ofM.

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