What is the limit as x approaches 0+of (x/(34))^x ?

The limit as x approaches 0+of (x/(34))^x is 1

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limit as x approaches 0+of (x/(34))^x

x \to 0 + lim ((\frac{x}{34})^{x})

1

Solution steps

x \to 0 + lim ((\frac{x}{34})^{x})

Apply exponent rule

= x \to 0 + lim (\frac{x ^{x}}{3 4 ^{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 +} ( x ^{x} )}{lim _{x \to 0 +} ( 3 4 ^{x} )}

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

x \to 0 + lim (3 4^{x}) = 1

= \frac{1}{1}

Simplify

= 1

\int_{0}^{16} \frac{1}{64 - x ^{2}} d x

y^{3} - (14 x + 4) + 3 x y^{2} y^{^{'}} = 0

y + y^{4} = (y^{6} + 3 x) \frac{d y}{d x}

y = (\frac{( 3 x ^{2} )}{( 2 x + 4 )})^{3}

x \to 2 + lim (1)

What is the limit as x approaches 0+of (x/(34))^x ?
The limit as x approaches 0+of (x/(34))^x is 1