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

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

= 5

x \to 5 - lim (\frac{6 x}{x - 5})

\int \frac{1}{x ^{7}} - x^{7} - \frac{1}{2} d x

\int 2 y 2 y - 3 d y

\frac{\partial}{\partial x} (x - 22)

\frac{d}{d x} ((x - 3)^{2} e^{2 x})

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