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

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

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limit as x approaches 0+of (e^{ax}+x)^{1/x}

x \to 0 + lim ((e^{a x} + x)^{\frac{1}{x}})

e^{a + 1}

Solution steps

x \to 0 + lim ((e^{a x} + x)^{\frac{1}{x}})

Apply exponent rules

= x \to 0 + lim (e^{\frac{1}{x} l n (e^{a x} + x)})

Apply the Limit Chain Rule:

e^{a + 1}

= e^{a + 1}

\frac{\partial}{\partial x} (\frac{y}{x - y})

\int_{1}^{\infty} x e^{- 7 x} d x

y^{^{'}} + 4 y = 6 e^{- 3 t}

y \to - 3 lim (\frac{y ^{2} - 9}{2 y ^{2} + 7 y + 3})

16 y^{^{''}} - y = 0, y (- 7) = 1, y^{^{'}} (- 7) = - 1

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