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

解答

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

4

求解步骤

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})

使用指数运算法则

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

使用极限链式法则:

1

= 4 \cdot 1

化简

= 4

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