What is the limit as x approaches 1 of (2x^3-14x^2+12x)/(x^3-10x^2+27x-18) ?

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limit as x approaches 1 of (2x^3-14x^2+12x)/(x^3-10x^2+27x-18)

x \to 1 lim (\frac{2 x ^{3} - 14 x ^{2} + 12 x}{x ^{3} - 10 x ^{2} + 27 x - 18})

- 1

Solution steps

x \to 1 lim (\frac{2 x ^{3} - 14 x ^{2} + 12 x}{x ^{3} - 10 x ^{2} + 27 x - 18})

Simplify

\frac{2 x ^{3} - 14 x ^{2} + 12 x}{x ^{3} - 10 x ^{2} + 27 x - 18} : \frac{2 x}{x - 3}

= x \to 1 lim (\frac{2 x}{x - 3})

Plug in the value

x = 1

= \frac{2 \cdot 1}{1 - 3}

Simplify

= - 1

x \cdot \frac{d y}{d x} + y = y^{2} x^{2} ln (x)

cos (a^{6} + x^{6})

\frac{d}{d x} (ln (b - a x))

cos (x), x = \frac{π}{2}

y^{^{''}} - \frac{1}{t} y^{^{'}} + \frac{26}{t ^{2}} y = 0

What is the limit as x approaches 1 of (2x^3-14x^2+12x)/(x^3-10x^2+27x-18) ?
The limit as x approaches 1 of (2x^3-14x^2+12x)/(x^3-10x^2+27x-18) is -1