Evaluate the following limits. lim_{xrightarrow-3}frac{sin(x+3)}{x^2+8x+15}

Evaluate the following limits. lim_{xrightarrow-3}frac{sin(x+3)}{x^2+8x+15}

Question
Limits and continuity
asked 2021-02-18
Evaluate the following limits.
\(\lim_{x\rightarrow-3}\frac{\sin(x+3)}{x^2+8x+15}\)

Answers (1)

2021-02-19
To evaluate
\(\lim_{x\rightarrow-3}\frac{\sin(x+3)}{x^2+8x+15}\)
Using, \(\lim_{x\rightarrow-3}\frac{\sin(x+3)}{x^2+8x+15}=\lim_{x\rightarrow-3}\frac{\sin(x+3)}{x^2+3x+5x+15}\)
\(=\lim_{x\rightarrow-3}\frac{\sin(x+3)}{x(x+3)+5(x+3)}\)
\(=\lim_{x\rightarrow-3}\frac{\sin(x+3)}{(x+3)(x+5)}\)
\(=\lim_{h\rightarrow0}[\frac{\sin h}{h}\times\frac{1}{h+2}]\)
\(=\frac{1}{2}\)
0

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