# Suppose u and v are vector functions that possess limits as t → a and let c be a constant. Prove the following properties of limits. (a) lim t → a [ u ( t ) + v ( t ) ] = lim t → a u ( t ) + lim t → a v ( t ) (b) lim t → a c u ( t ) = c lim t → a u ( t ) (c) lim t → a [ u ( t ) ⋅ v ( t ) ] = lim t → a u ( t ) ⋅ lim t → a v ( t ) (d) lim t → a [ u ( t ) × v ( t ) ] = lim t → a u ( t ) × lim t → a v ( t )

### Calculus (MindTap Course List)

8th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781285740621

### Calculus (MindTap Course List)

8th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781285740621

#### Solutions

Chapter 13.1, Problem 53E
Textbook Problem

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