What is the limit as x approaches 0 of ((1-x)^5-1)/x ?

The limit as x approaches 0 of ((1-x)^5-1)/x is -5

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limit as x approaches 0 of ((1-x)^5-1)/x

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

- 5

Solution steps

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

Simplify

\frac{( 1 - x ) ^{5} - 1}{x} : x - (- x + 1)^{4} - (- x + 1)^{3} - (- x + 1)^{2} - 2

= x \to 0 lim (x - (- x + 1)^{4} - (- x + 1)^{3} - (- x + 1)^{2} - 2)

Plug in the value

x = 0

= 0 - (- 0 + 1)^{4} - (- 0 + 1)^{3} - (- 0 + 1)^{2} - 2

Simplify

0 - (- 0 + 1)^{4} - (- 0 + 1)^{3} - (- 0 + 1)^{2} - 2 : - 5

= - 5

x \to 2 lim (4 x + 3)

x \to 2 lim (4 x + 2)

x \to 0 lim (6 tan (x))

x \to 8 lim (\frac{4 x - 2}{9})

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

What is the limit as x approaches 0 of ((1-x)^5-1)/x ?
The limit as x approaches 0 of ((1-x)^5-1)/x is -5