What is the limit as x approaches-6 of (x^2+15x+54)/(-54-3x+x^2) ?

The limit as x approaches-6 of (x^2+15x+54)/(-54-3x+x^2) is -1/5

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limit as x approaches-6 of (x^2+15x+54)/(-54-3x+x^2)

x \to - 6 lim (\frac{x ^{2} + 15 x + 54}{- 54 - 3 x + x ^{2}})

- \frac{1}{5}

Decimal

- 0.2

Solution steps

x \to - 6 lim (\frac{x ^{2} + 15 x + 54}{- 54 - 3 x + x ^{2}})

Simplify

\frac{x ^{2} + 15 x + 54}{- 54 - 3 x + x ^{2}} : \frac{x + 9}{x - 9}

= x \to - 6 lim (\frac{x + 9}{x - 9})

Plug in the value

x = - 6

= \frac{- 6 + 9}{- 6 - 9}

Simplify

\frac{- 6 + 9}{- 6 - 9} : - \frac{1}{5}

= - \frac{1}{5}

x \to 0 - lim (\frac{2}{sin ( x )})

x \to - d lim (2 x^{3} + 3 x - 1)

x \to 3 lim (\frac{2 x - 11}{x - 3})

x \to \infty lim (ln (3 x^{2} + 2) - ln (x^{2}))

x \to \infty lim ([x sin (\frac{1}{x})])

What is the limit as x approaches-6 of (x^2+15x+54)/(-54-3x+x^2) ?
The limit as x approaches-6 of (x^2+15x+54)/(-54-3x+x^2) is -1/5