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

The limit as x approaches 0-of (4-4/x)^x is 1

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limit as x approaches 0-of (4-4/x)^x

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

1

Solution steps

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

Apply exponent rules

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

Apply the Limit Chain Rule:

1

= 1

x \to 4 lim (7^{2} + 12 x)

x \to 0 + lim (- 4 x ln (5 x))

x \to 0 lim (\frac{x ^{3} + 4}{x ^{2}})

x \to 0 lim (\frac{3 x + 4}{x})

x \to π lim (cos (9 x))

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