What is the limit as x approaches-1 of (x^7+1)/(x+1) ?

The limit as x approaches-1 of (x^7+1)/(x+1) is 7

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limit as x approaches-1 of (x^7+1)/(x+1)

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

7

Solution steps

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

Simplify

\frac{x ^{7} + 1}{x + 1} : x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1

= x \to - 1 lim (x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1)

Plug in the value

x = - 1

= (- 1)^{6} - (- 1)^{5} + (- 1)^{4} - (- 1)^{3} + (- 1)^{2} - (- 1) + 1

Simplify

(- 1)^{6} - (- 1)^{5} + (- 1)^{4} - (- 1)^{3} + (- 1)^{2} - (- 1) + 1 : 7

= 7

\int (x^{6} + 1) e^{x^{7} + 7 x} d x

\int \frac{arcsin ( 2 x )}{1 - 4 x ^{2}} d x

f (x) = x + 5, at x = - 4

\int tan^{2} (5 x) sec^{4} (5 x) d x

\frac{d}{d t} (\frac{( t + 1 ) ^{2}}{( t - 1 ) ^{2}})

What is the limit as x approaches-1 of (x^7+1)/(x+1) ?
The limit as x approaches-1 of (x^7+1)/(x+1) is 7