What is the limit as x approaches 0+of ax^{x^2} ?

The limit as x approaches 0+of ax^{x^2} is a

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limit as x approaches 0+of ax^{x^2}

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

a

Solution steps

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

x \to a lim [c \cdot f (x)] = c \cdot x \to a lim f (x)

= a \cdot x \to 0 + lim (x^{x^{2}})

Apply exponent rules

= a \cdot x \to 0 + lim (e^{x^{2} l n (x)})

Apply the Limit Chain Rule:

1

= a \cdot 1

Simplify

= a

x \to 3 lim (4 x^{3} - 5 x^{2} + x - 8)

\int sec^{2} (x) - csc (x) cot (x) d x

x \to - 3 lim (f (x) x)

\int \frac{4 x}{16 - x ^{4}} d x

y^{^{'}} = 8 y^{2} cos (t) + 7 y^{2} sin (4 t)

What is the limit as x approaches 0+of ax^{x^2} ?
The limit as x approaches 0+of ax^{x^2} is a