What is the limit as x approaches 0+of (ax)^{bx} ?

The limit as x approaches 0+of (ax)^{bx} is 1

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limit as x approaches 0+of (ax)^{bx}

x \to 0 + lim ((a x)^{b x})

1

Solution steps

x \to 0 + lim ((a x)^{b x})

Apply exponent rules

= x \to 0 + lim (e^{b x l n (a x)})

Apply the Limit Chain Rule:

1

= 1

x \to 0 lim (x \cdot sin (\frac{2}{x}))

x \to 1 lim (x - x^{2})

x \to 3 lim (ln (e^{3 x}))

x \to 5 lim (x^{3} + 3 x^{2} + x)

x \to 2 lim (lo g_{2} (x))

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