What is the limit as x approaches 0+of 4(sin(x))^x ?

The limit as x approaches 0+of 4(sin(x))^x is 4

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limit as x approaches 0+of 4(sin(x))^x

x \to 0 + lim (4 (sin (x))^{x})

4

Solution steps

x \to 0 + lim (4 (sin (x))^{x})

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

= 4 \cdot x \to 0 + lim ((sin (x))^{x})

Apply exponent rules

= 4 \cdot x \to 0 + lim (e^{x l n (s i n (x))})

Apply the Limit Chain Rule:

1

= 4 \cdot 1

Simplify

= 4

x \to 0 + lim (\frac{ln ( 5 x )}{x})

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

x \to 2 lim (tan^{2} (\frac{π}{8} x))

x \to 0 lim (tan^{2} (7 x))

x \to - \infty lim (3^{x} \cdot x)

What is the limit as x approaches 0+of 4(sin(x))^x ?
The limit as x approaches 0+of 4(sin(x))^x is 4