What is the limit as x approaches 1 of (x^3-x)/(x-1) ?

The limit as x approaches 1 of (x^3-x)/(x-1) is 2

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limit as x approaches 1 of (x^3-x)/(x-1)

x \to 1 lim (\frac{x ^{3} - x}{x - 1})

2

Solution steps

x \to 1 lim (\frac{x ^{3} - x}{x - 1})

Simplify

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

= x \to 1 lim (x (x + 1))

Plug in the value

x = 1

= 1 \cdot (1 + 1)

Simplify

= 2

x \to 0 lim (- \frac{1}{3 x ^{3}})

\int 3 cos (4 x) d x

y^{^{'}} - \frac{x}{1 + x ^{2}} y = x

y^{^{''}} + 4 y = 6 sin (2 x)

(5 x + 13 y) d x + (13 x + 6 y) d y = 0, y (0) = 2

What is the limit as x approaches 1 of (x^3-x)/(x-1) ?
The limit as x approaches 1 of (x^3-x)/(x-1) is 2