What is the limit as x approaches 0 of (1+6x)^{7/x} ?

The limit as x approaches 0 of (1+6x)^{7/x} is e^{42}

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limit as x approaches 0 of (1+6x)^{7/x}

x \to 0 lim ((1 + 6 x)^{\frac{7}{x}})

e^{42}

Decimal Notation

1.73927 E 18

Solution steps

x \to 0 lim ((1 + 6 x)^{\frac{7}{x}})

Apply exponent rules

= x \to 0 lim (e^{\frac{7}{x} l n (1 + 6 x)})

Apply the Limit Chain Rule:

e^{42}

= e^{42}

2 x - tan (x)

k = 1 \sum \infty \frac{1}{k + 6}

f (x) = \frac{3 x}{4 - x ^{2}}, at x = 1

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

x \to 7 + lim (x + 2)

What is the limit as x approaches 0 of (1+6x)^{7/x} ?
The limit as x approaches 0 of (1+6x)^{7/x} is e^{42}