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

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

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

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

e^{3}

Decimal

20.08553 \dots

Solution steps

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

x \to a - lim f (x) = x \to a + lim f (x) = L

then

x \to a lim f (x) = L

x \to 0 - lim ((1 + sin (3 x))^{\frac{1}{x}}) = e^{3}

x \to 0 + lim ((1 + sin (3 x))^{\frac{1}{x}}) = e^{3}

= e^{3}

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