What is the limit as x approaches 0 of (e^x+x)^{5/x} ?

The limit as x approaches 0 of (e^x+x)^{5/x} is e^{10}

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limit as x approaches 0 of (e^x+x)^{5/x}

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

e^{10}

Decimal Notation

22026.46579 \dots

Solution steps

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

Apply exponent rules

= x \to 0 lim (e^{\frac{5}{x} l n (e^{x} + x)})

Apply the Limit Chain Rule:

e^{10}

= e^{10}

\int sin^{2} (2 π x) d x

x \to - 2 lim (\frac{x - 2}{∣ x - 2 ∣})

x \to 0 lim (\frac{cos ( π x )}{x})

t e^{- 3 t}

\frac{d}{d x} ((x^{3} - 1)^{100})

What is the limit as x approaches 0 of (e^x+x)^{5/x} ?
The limit as x approaches 0 of (e^x+x)^{5/x} is e^{10}