What is the limit as x approaches 3 of ((2x^3-5x^2-2x-3))/(4x^3-13x^2+4x-3) ?

The limit as x approaches 3 of ((2x^3-5x^2-2x-3))/(4x^3-13x^2+4x-3) is 11/17

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limit as x approaches 3 of ((2x^3-5x^2-2x-3))/(4x^3-13x^2+4x-3)

x \to 3 lim (\frac{( 2 x ^{3} - 5 x ^{2} - 2 x - 3 )}{4 x ^{3} - 13 x ^{2} + 4 x - 3})

\frac{11}{17}

Decimal Notation

0.64705 \dots

Solution steps

x \to 3 lim (\frac{2 x ^{3} - 5 x ^{2} - 2 x - 3}{4 x ^{3} - 13 x ^{2} + 4 x - 3})

Simplify

\frac{2 x ^{3} - 5 x ^{2} - 2 x - 3}{4 x ^{3} - 13 x ^{2} + 4 x - 3} : \frac{2 x ^{2} + x + 1}{4 x ^{2} - x + 1}

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

Plug in the value

x = 3

= \frac{2 \cdot 3 ^{2} + 3 + 1}{4 \cdot 3 ^{2} - 3 + 1}

Simplify

\frac{2 \cdot 3 ^{2} + 3 + 1}{4 \cdot 3 ^{2} - 3 + 1} : \frac{11}{17}

= \frac{11}{17}

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

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

f (θ) = 4 sin (θ)

y = \frac{14}{x}, y = - 64 x + 72

\frac{\partial}{\partial y} (4 x^{3} y^{3} - 3 x^{2} sin (x^{3}) y)

What is the limit as x approaches 3 of ((2x^3-5x^2-2x-3))/(4x^3-13x^2+4x-3) ?
The limit as x approaches 3 of ((2x^3-5x^2-2x-3))/(4x^3-13x^2+4x-3) is 11/17