What is the limit as x approaches 1 of (x-x^4)/(1-x) ?

The limit as x approaches 1 of (x-x^4)/(1-x) is 3

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limit as x approaches 1 of (x-x^4)/(1-x)

x \to 1 lim (\frac{x - x ^{4}}{1 - x})

3

Solution steps

x \to 1 lim (\frac{x - x ^{4}}{1 - x})

Simplify

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

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

Plug in the value

x = 1

= 1 \cdot (1^{2} + 1 + 1)

Simplify

= 3

x \to \infty lim (\frac{1 + x}{3 1 + x})

x \to \infty lim (\frac{e ^{5 x}}{3 - e ^{2 x}})

x \to 0 lim (x cos (2 x))

x \to 0 lim (sin (x) cos (x))

x \to \infty lim (- 8 (\frac{3}{x}))

What is the limit as x approaches 1 of (x-x^4)/(1-x) ?
The limit as x approaches 1 of (x-x^4)/(1-x) is 3