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Please find the following limit lim(x->inf) (x+2/x+1) x

Please find the following limit
lim(x->inf) (x+2/x+1)x

Grade:11

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
9 years ago
Ans:Hello student, please find answer to your question
L = \lim_{x\rightarrow \infty }(\frac{x+2}{x+1})^{x}
L = \lim_{x\rightarrow \infty }(1+\frac{1}{x+1})^{x}
L = \lim_{x\rightarrow \infty }(1+\frac{1}{x+1})^{\frac{x+1}{x+1}.x}
L = \lim_{x\rightarrow \infty }(1+\frac{1}{x+1})^{\frac{1}{x+1}} = e
L = e^{\lim_{x\rightarrow \infty }{\frac{x}{x+1}}}
L = e^1 = e

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