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Illustrate how the product law, difference law, constant multiple law, and identity law are used to evaluate lim (2y- 32) (.y.)-(4. 1, -3)

Illustrate how the product law, difference law, constant multiple law, and identity law are used to evaluate lim (2y- 32) (.y.)-(4. 1, -3)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Illustrate how the product law, difference law, constant multiple law, and identity law are used to evaluate (1y - 32) lim (x.y.)-(4. 1. -3)
Transcribed Image Text:Illustrate how the product law, difference law, constant multiple law, and identity law are used to evaluate (1y - 32) lim (x.y.)-(4. 1. -3)
Expert Solution
Step 1 Introduction

We Know that 

Limit Laws :

Let f(x) and g(x) be defined for all x\ne a over some open interval containing a. Assume that L and M are real numbers such that \underset{x\to a}{\lim}f(x)=L and \underset{x\to a}{\lim}g(x)=M. Let c be a constant. Then, each of the following statements holds:

Identity law for limits: 

For any real number a and any constant c,

  1. \underset{x\to a}{\lim}x=a
  2. \underset{x\to a}{\lim}c=c

Difference law for limits: \underset{x\to a}{\lim}(f(x)-g(x))=\underset{x\to a}{\lim}f(x)-\underset{x\to a}{\lim}g(x)=L-M

Constant multiple law for limits: \underset{x\to a}{\lim}cf(x)=c \cdot \underset{x\to a}{\lim}f(x)=cL

Product law for limits: \underset{x\to a}{\lim}(f(x) \cdot g(x))=\underset{x\to a}{\lim}f(x) \cdot \underset{x\to a}{\lim}g(x)=L \cdot M

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