What is the limit as x approaches 0 of (1+8x)^{5/x} ?

The limit as x approaches 0 of (1+8x)^{5/x} is e^{40}

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limit as x approaches 0 of (1+8x)^{5/x}

x \to 0 lim ((1 + 8 x)^{\frac{5}{x}})

e^{40}

Decimal

2.35385 E 17

Solution steps

x \to 0 lim ((1 + 8 x)^{\frac{5}{x}})

Apply exponent rules

= x \to 0 lim (e^{\frac{5}{x} l n (1 + 8 x)})

Apply the Limit Chain Rule:

e^{40}

= e^{40}

\frac{d ^{2}}{d r ( θ ) d θ} (r (θ) sin (θ))

cos (x^{2}) - 2 x^{2} sin (x^{2})

\frac{d y}{d t} = (y - sin (t)) + cos (t)

6 x, x^{2}

\int 8 e^{- 8 x} d x

What is the limit as x approaches 0 of (1+8x)^{5/x} ?
The limit as x approaches 0 of (1+8x)^{5/x} is e^{40}