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Solve lim(x->0) (x 2 +x+1/x 2 +x+2) 1/x

Solve 
lim(x->0) (x2+x+1/x2+x+2)1/x
 

Grade:12

1 Answers

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

L = \lim_{x\rightarrow 0}(\frac{x^2+x+1}{x^2+x+2})^{1/x}
L = (\frac{1}{2})^{\lim_{x\rightarrow 0}\frac{1}{x}}
L = (\frac{1}{2})^{\lim_{x\rightarrow 0^{-}}\frac{1}{x}}
L = \infty
L = (\frac{1}{2})^{\lim_{x\rightarrow 0^{+}}\frac{1}{x}}
L =0
So the limit does not exist.

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