What is the limit as x approaches 1 of (sqrt(17-x^2)-4)/(x-1) ?

The limit as x approaches 1 of (sqrt(17-x^2)-4)/(x-1) is -1/4

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limit as x approaches 1 of (sqrt(17-x^2)-4)/(x-1)

x \to 1 lim (\frac{17 - x ^{2} - 4}{x - 1})

- \frac{1}{4}

Decimal Notation

- 0.25

Solution steps

x \to 1 lim (\frac{17 - x ^{2} - 4}{x - 1})

Multiply by the conjugate of

17 - x^{2} - 4 : \frac{- x ^{2} + 1}{17 - x ^{2} + 4}

= x \to 1 lim \frac{\frac{- x ^{2} + 1}{17 - x ^{2} + 4}}{x - 1}

Simplify

\frac{\frac{- x ^{2} + 1}{17 - x ^{2} + 4}}{x - 1} : - \frac{x + 1}{- x ^{2} + 17 + 4}

= x \to 1 lim (- \frac{x + 1}{- x ^{2} + 17 + 4})

Plug in the value

x = 1

= - \frac{1 + 1}{- 1 ^{2} + 17 + 4}

Simplify

- \frac{1 + 1}{- 1 ^{2} + 17 + 4} : - \frac{1}{4}

= - \frac{1}{4}

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What is the limit as x approaches 1 of (sqrt(17-x^2)-4)/(x-1) ?
The limit as x approaches 1 of (sqrt(17-x^2)-4)/(x-1) is -1/4