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

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

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

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

3

Solution steps

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

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

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

Apply exponent rules

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

Apply the Limit Chain Rule:

1

= 3 \cdot 1

Simplify

= 3

x \to \frac{2}{3} lim (3 x (2 x - 1))

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

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

x \to \frac{1}{3} lim (\frac{arcsin ( x ) - arcsin ( \frac{1}{3} )}{x - \frac{1}{3}})

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

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