What is the limit as x approaches 5 of ((13-sqrt(4x^2+69)))/(x-5) ?

The limit as x approaches 5 of ((13-sqrt(4x^2+69)))/(x-5) is -20/13

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limit as x approaches 5 of ((13-sqrt(4x^2+69)))/(x-5)

x \to 5 lim (\frac{( 13 - 4 x ^{2} + 69 )}{x - 5})

- \frac{20}{13}

Decimal

- 1.53846 \dots

Solution steps

x \to 5 lim (\frac{13 - 4 x ^{2} + 69}{x - 5})

Rationalize numerator

\frac{13 - 4 x ^{2} + 69}{x - 5} : - \frac{4 ( x + 5 )}{4 x ^{2} + 69 + 13}

= x \to 5 lim (- \frac{4 ( x + 5 )}{4 x ^{2} + 69 + 13})

Plug in the value

x = 5

= - \frac{4 ( 5 + 5 )}{4 \cdot 5 ^{2} + 69 + 13}

Simplify

- \frac{4 ( 5 + 5 )}{4 \cdot 5 ^{2} + 69 + 13} : - \frac{20}{13}

= - \frac{20}{13}

What is the limit as x approaches 5 of ((13-sqrt(4x^2+69)))/(x-5) ?
The limit as x approaches 5 of ((13-sqrt(4x^2+69)))/(x-5) is -20/13