What is the limit as x approaches 0 of (1+9x)^{1/x} ?

The limit as x approaches 0 of (1+9x)^{1/x} is e^9

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limit as x approaches 0 of (1+9x)^{1/x}

x \to 0 lim ((1 + 9 x)^{\frac{1}{x}})

e^{9}

Decimal

8103.08392 \dots

Solution steps

x \to 0 lim ((1 + 9 x)^{\frac{1}{x}})

Apply exponent rules

= x \to 0 lim (e^{\frac{1}{x} l n (1 + 9 x)})

Apply the Limit Chain Rule:

e^{9}

= e^{9}

x \to 4 lim (\frac{3}{( 4 - x ) ^{3}})

x \to 0 + lim (x x)

x \to 8 lim (\frac{x ^{2}}{x - 8})

x \to 3 lim (5 f (x))

x \to 0 lim (- 5)

What is the limit as x approaches 0 of (1+9x)^{1/x} ?
The limit as x approaches 0 of (1+9x)^{1/x} is e^9