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Solve lim(x->inf) [x 2 +x+1/2x 2 +x+1] sinx/x

Solve
lim(x->inf) [x2+x+1/2x2+x+1]sinx/x

Grade:12

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
7 years ago
Ans:
Hello Student,
Please find answer to your question below

L = \lim_{x\rightarrow \infty }(\frac{x^2+x+1}{2x^2+x+1})^{\frac{1}{x}}
L = \lim_{x\rightarrow \infty }(\frac{1+\frac{1}{x}+\frac{1}{x^2}}{2+\frac{1}{x}+\frac{1}{x^2}})^{\frac{1}{x}}
L = (\frac{1}{2})^{\lim_{x\rightarrow \infty }\frac{1}{x}}
L = (\frac{1}{2})^{0}
L = 1

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