What is the limit as x approaches 0+of (1/x)^{3x} ?

The limit as x approaches 0+of (1/x)^{3x} is 1

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limit as x approaches 0+of (1/x)^{3x}

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

1

Solution steps

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

Apply exponent rule

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

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 +} ( x ^{3 x} )}

x \to 0 + lim (1) = 1

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

= \frac{1}{1}

Simplify

= 1

What is the limit as x approaches 0+of (1/x)^{3x} ?
The limit as x approaches 0+of (1/x)^{3x} is 1