What is the limit as x approaches-1/2 of (2x^2+7x+3)/(2x^2+3x+1) ?

The limit as x approaches-1/2 of (2x^2+7x+3)/(2x^2+3x+1) is 5

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limit as x approaches-1/2 of (2x^2+7x+3)/(2x^2+3x+1)

x \to - \frac{1}{2} lim (\frac{2 x ^{2} + 7 x + 3}{2 x ^{2} + 3 x + 1})

5

Solution steps

x \to - \frac{1}{2} lim (\frac{2 x ^{2} + 7 x + 3}{2 x ^{2} + 3 x + 1})

Simplify

\frac{2 x ^{2} + 7 x + 3}{2 x ^{2} + 3 x + 1} : \frac{x + 3}{x + 1}

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

Plug in the value

x = - \frac{1}{2}

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

Simplify

\frac{- \frac{1}{2} + 3}{- \frac{1}{2} + 1} : 5

= 5

What is the limit as x approaches-1/2 of (2x^2+7x+3)/(2x^2+3x+1) ?
The limit as x approaches-1/2 of (2x^2+7x+3)/(2x^2+3x+1) is 5