What is the limit as x approaches 1 of (x^4+3x^3-13x^2-27x+36)/(x^2+3x-4) ?

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limit as x approaches 1 of (x^4+3x^3-13x^2-27x+36)/(x^2+3x-4)

x \to 1 lim (\frac{x ^{4} + 3 x ^{3} - 13 x ^{2} - 27 x + 36}{x ^{2} + 3 x - 4})

- 8

Solution steps

x \to 1 lim (\frac{x ^{4} + 3 x ^{3} - 13 x ^{2} - 27 x + 36}{x ^{2} + 3 x - 4})

Simplify

\frac{x ^{4} + 3 x ^{3} - 13 x ^{2} - 27 x + 36}{x ^{2} + 3 x - 4} : (x + 3) (x - 3)

= x \to 1 lim ((x + 3) (x - 3))

Plug in the value

x = 1

= (1 + 3) (1 - 3)

Simplify

= - 8

What is the limit as x approaches 1 of (x^4+3x^3-13x^2-27x+36)/(x^2+3x-4) ?
The limit as x approaches 1 of (x^4+3x^3-13x^2-27x+36)/(x^2+3x-4) is -8