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

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

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

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

1

Solution steps

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

x \to a lim [f (x) \pm g (x)] = x \to a lim f (x) \pm x \to a lim g (x)

With the exception of indeterminate form

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

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

x \to 0 + lim (1) = 1

= 0 + 1

Simplify

= 1

x \to 0 lim (\frac{( 1 - cos ( x ) )}{7 x \cdot sin ( x )})

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

x \to 0 + lim (4 (csc (x) - \frac{1}{x}))

x \to 0 lim (\frac{arccos ( x )}{x})

x \to 3 + lim (\frac{3 x - 10}{3 - x})

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