What is the limit as x approaches 2 of (x^3+x^2-8x-12)/(x^4+4x^3+5x^2+4x+4) ?

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limit as x approaches 2 of (x^3+x^2-8x-12)/(x^4+4x^3+5x^2+4x+4)

x \to 2 lim (\frac{x ^{3} + x ^{2} - 8 x - 12}{x ^{4} + 4 x ^{3} + 5 x ^{2} + 4 x + 4})

- \frac{1}{5}

Decimal

- 0.2

Solution steps

x \to 2 lim (\frac{x ^{3} + x ^{2} - 8 x - 12}{x ^{4} + 4 x ^{3} + 5 x ^{2} + 4 x + 4})

Plug in the value

x = 2

= \frac{2 ^{3} + 2 ^{2} - 8 \cdot 2 - 12}{2 ^{4} + 4 \cdot 2 ^{3} + 5 \cdot 2 ^{2} + 4 \cdot 2 + 4}

Simplify

\frac{2 ^{3} + 2 ^{2} - 8 \cdot 2 - 12}{2 ^{4} + 4 \cdot 2 ^{3} + 5 \cdot 2 ^{2} + 4 \cdot 2 + 4} : - \frac{1}{5}

= - \frac{1}{5}

y^{^{'}} = \frac{( t ^{4} + y ^{4} )}{t y ^{3}}

x \to + 0 lim (x)

\int (2 x + 3)^{4} d x

\int e^{uv} d u

\frac{d}{d x} (4 x^{5} - 10 x^{4} + 2)

What is the limit as x approaches 2 of (x^3+x^2-8x-12)/(x^4+4x^3+5x^2+4x+4) ?
The limit as x approaches 2 of (x^3+x^2-8x-12)/(x^4+4x^3+5x^2+4x+4) is -1/5