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

- 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}

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\frac{d ^{2} y}{d x ^{2}} + 2 \frac{d y}{d x} - 3 y = 2 x - 17

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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