Sine limits Evaluate the following limits.a.

Chapter 9, Problem 60AE

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QUESTION:

Sine limits  Evaluate the following limits.

(a) \(\lim _{(x, y) \rightarrow(0.0)} \frac{\sin (x+y)}{x+y}\)

(b) \(\lim _{(x, y) \rightarrow(0,0)} \frac{\sin x+\sin y}{x+y}\)

Questions & Answers

QUESTION:

Sine limits  Evaluate the following limits.

(a) \(\lim _{(x, y) \rightarrow(0.0)} \frac{\sin (x+y)}{x+y}\)

(b) \(\lim _{(x, y) \rightarrow(0,0)} \frac{\sin x+\sin y}{x+y}\)

ANSWER:

Solution of equation a  :

Step 1:

Formula of Sin(a+b) =  sina.cosb +cosa.sinb

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