BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805
BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

Solutions

Chapter 3.3, Problem 45E
To determine

Find the given limit using formula 2 .

Expert Solution

Answer to Problem 45E

The limθ0sinθθ+tanθ=12 .

Explanation of Solution

Given:

The given limitis limθ0sinθθ+tanθ .

Calculation:

  limθ0sinθθ+tanθ=limθ0sinθθθθ+tanθ=limθ0sinθθ1θ+tanθθ=limθ0sinθθ1θθ+tanθθ=limθ0sinθθ1limθ01+limθ0tanθθ=limθ0sinθθ1limθ01+limθ0sinθθ1cosθ=limθ0sinθθ11+limθ0sinθθlimθ01cosθ

Use limit formula limx0sinxx=1 .

  =111+11=12

Hence the value of the limθ0sinθθ+tanθ=12 .

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