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}

sin (t + \frac{11 π}{2})

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

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

y^{^{''}} + 6 y^{^{'}} - 7 y = 0

\int 5 e^{x} sec (e^{x} + 2) d 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