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

The limit as x approaches 0+of (e^x+x)^{3/x} is e^6

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

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

e^{6}

Decimal

403.42879 \dots

Solution steps

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

Apply exponent rules

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

Apply the Limit Chain Rule:

e^{6}

= e^{6}

\int \frac{1}{x ^{2} + 2 x + 3} d x

\frac{d y}{d x} = \frac{x}{1 + 2 y}

f (x) = \frac{x ^{3}}{3} + 2 x^{2} + 13 x - 5

n = 1 \sum \infty \frac{n}{ln ( 2 n )}

x^{3} - 2 x + 2, at x = 3, y = 21

What is the limit as x approaches 0+of (e^x+x)^{3/x} ?
The limit as x approaches 0+of (e^x+x)^{3/x} is e^6