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

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

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

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

0

Solution steps

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

Plug in the value

x = 0

= 0 \cdot (\frac{1}{3})^{0}

Simplify

= 0

x \to 0 lim (\frac{6 x ^{2} + 1 x}{x})

x \to 4 lim (x^{4} + 3 x^{3} - x)

x \to 2 + lim (\frac{x}{x + 2})

x \to 0 lim (\frac{x ^{2} + 9 x}{x})

x \to 0 + lim (x \cdot cot (x))

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