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

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

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

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

1

Solution steps

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

Simplify

(3 x)^{s i n (x)} : 3^{s i n (x)} x^{s i n (x)}

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

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

With the exception of indeterminate form

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

x \to 0 + lim (3^{s i n (x)}) = 1

x \to 0 + lim (x^{s i n (x)}) = 1

= 1 \cdot 1

Simplify

= 1

25 y^{^{''}} - 40 y^{^{'}} + 16 y = 0, y (0) = 2, y^{^{'}} (0) = - 3

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