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

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

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

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

1

Solution steps

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

Apply exponent rules

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

Apply the Limit Chain Rule:

1

= 1

\int (\frac{1}{4})^{x + 1} d x

\int \frac{x ^{2}}{( x - 1 ) ^{2}} d x

\int (\frac{x}{1 + x ^{2}})^{2} d x

\int \frac{1}{x ^{a}} d x

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

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