What is the limit as x approaches+0+of e^{-2/(x^3)} ?

The limit as x approaches+0+of e^{-2/(x^3)} is 0

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limit as x approaches+0+of e^{-2/(x^3)}

x \to + 0 + lim (e^{- \frac{2}{x ^{3}}})

0

Solution steps

x \to 0 + lim (e^{- \frac{2}{x ^{3}}})

Simplify

e^{- \frac{2}{x ^{3}}} : \frac{1}{e ^{\frac{2}{x ^{3}}}}

= x \to 0 + lim (\frac{1}{e ^{\frac{2}{x ^{3}}}})

x \to a lim [\frac{f ( x )}{g ( x )}] = \frac{lim _{x \to a} f ( x )}{lim _{x \to a} g ( x )}, x \to a lim g (x) \neq = 0

With the exception of indeterminate form

= \frac{lim _{x \to 0 +} ( 1 )}{lim _{x \to 0 +} ( e ^{\frac{2}{x ^{3}}} )}

x \to 0 + lim (1) = 1

x \to 0 + lim (e^{\frac{2}{x ^{3}}}) = \infty

= \frac{1}{\infty}

Apply Infinity Property:

\frac{c}{\infty} = 0

= 0

f (x) = \frac{x ^{2}}{cos ( x )}

f (x) = tan (5 x)

\int sec^{- \frac{1}{2}} (x) tan^{3} (x) d x

\int cot (13 x) d x

\int sin^{3} (x) sin (3 x) d x

What is the limit as x approaches+0+of e^{-2/(x^3)} ?
The limit as x approaches+0+of e^{-2/(x^3)} is 0