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

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

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

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

5

Solution steps

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

Simplify

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

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

Plug in the value

x = 1

= 1^{4} + 1^{3} + 1^{2} + 1 + 1

Simplify

= 5

f (x) = x sin (2^{x})

\frac{1}{x} e^{y} tan (y) y^{^{'}} = e^{x + y}

\frac{\partial}{\partial y} (\frac{4 x}{x ^{2} + y ^{2}})

\int \frac{1}{2} (cos (x))^{2} d x

f (x) = \frac{40}{x}, (1, 40)

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