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

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

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

x \to 0 + lim (x^{s i n (3 x)})

1

Solution steps

x \to 0 + lim (x^{s i n (3 x)})

Apply exponent rules

= x \to 0 + lim (e^{s i n (3 x) l n (x)})

Apply the Limit Chain Rule:

1

= 1

\int (1 - cos (\frac{t}{2}))^{2} sin (\frac{t}{2}) d t

\int 2 x e^{2 x^{2}} d x

\frac{d y}{d x} = y - x^{2}

y^{^{''}} - 10 y^{^{'}} + 25 = 0

\frac{d}{d x} ((\frac{cos ( x )}{1 + sin ( x )})^{5})

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