What is the limit as x approaches 2 of ((3x-6))/(1-sqrt(4x-7)) ?

The limit as x approaches 2 of ((3x-6))/(1-sqrt(4x-7)) is -3/2

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limit as x approaches 2 of ((3x-6))/(1-sqrt(4x-7))

x \to 2 lim (\frac{( 3 x - 6 )}{1 - 4 x - 7})

- \frac{3}{2}

Decimal Notation

- 1.5

Solution steps

x \to 2 lim (\frac{3 x - 6}{1 - 4 x - 7})

Rationalize denominator

\frac{3 x - 6}{1 - 4 x - 7} : - \frac{3 ( 4 x - 7 + 1 )}{4}

= x \to 2 lim (- \frac{3 ( 4 x - 7 + 1 )}{4})

Plug in the value

x = 2

= - \frac{3 ( 4 \cdot 2 - 7 + 1 )}{4}

Simplify

- \frac{3 ( 4 \cdot 2 - 7 + 1 )}{4} : - \frac{3}{2}

= - \frac{3}{2}

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

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

\int \frac{1}{( x + 2 ) ( x ^{2} + 1 )} d x

f (x) = x - 2, at x = 3

cos (2 x) + sin (x)

What is the limit as x approaches 2 of ((3x-6))/(1-sqrt(4x-7)) ?
The limit as x approaches 2 of ((3x-6))/(1-sqrt(4x-7)) is -3/2