What is the limit as x approaches 0 of (1-4x)^{7/x} ?

The limit as x approaches 0 of (1-4x)^{7/x} is 1/(e^{28)}

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limit as x approaches 0 of (1-4x)^{7/x}

x \to 0 lim ((1 - 4 x)^{\frac{7}{x}})

\frac{1}{e ^{28}}

Decimal Notation

6.9144 E - 13

Solution steps

x \to 0 lim ((1 - 4 x)^{\frac{7}{x}})

Apply exponent rules

= x \to 0 lim (e^{\frac{7}{x} l n (1 - 4 x)})

Apply the Limit Chain Rule:

\frac{1}{e ^{28}}

= \frac{1}{e ^{28}}

n = 1 \sum \infty \frac{35}{- 6 ^{n}}

\int sin (\frac{θ}{2}) d θ

y^{^{''}} - 9 y = (x^{2} - 5) sin (3 x)

y = 7 x, y = x^{2} - 8, y = 0

\frac{d y}{d x} = 2 x + x y

What is the limit as x approaches 0 of (1-4x)^{7/x} ?
The limit as x approaches 0 of (1-4x)^{7/x} is 1/(e^{28)}