What is the limit as x approaches 2 of (3-sqrt(4x+1))/((x^2-2x)) ?

The limit as x approaches 2 of (3-sqrt(4x+1))/((x^2-2x)) is -1/3

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limit as x approaches 2 of (3-sqrt(4x+1))/((x^2-2x))

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

- \frac{1}{3}

Decimal

- 0.33333 \dots

Solution steps

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

Rationalize numerator

\frac{3 - 4 x + 1}{x ^{2} - 2 x} : - \frac{4}{x ( 4 x + 1 + 3 )}

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

Plug in the value

x = 2

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

Simplify

- \frac{4}{2 ( 4 \cdot 2 + 1 + 3 )} : - \frac{1}{3}

= - \frac{1}{3}

y^{^{'}} = \frac{6 x ^{5} y}{ln ( y )}

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

t \to 0 lim (\frac{e ^{t} - t - 1}{t})

\int_{0}^{2} π (e^{- x^{2}})^{2} d x

d er i v a t i v e f (x) = 7 e^{x} cos (x)

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