Solve lim(x->0) (x2+x+1/x2+x+2)1/x

Ans:Hello Student,Please find answer to your question belowSo the limit does not exist.

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Grade 12Integral Calculus

Solve
lim(x->0) (x²+x+1/x²+x+2)^1/x

Lovey

11 Years agoGrade 12

1 Answer

Jitender Singh

11 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.