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Question: The value of \(\lim_{x \rightarrow 7}\frac{2 - \sqrt{x - 3}}{x^{2} - 49}\) is...

The value of lim⁡x→72−x−3x2−49\lim_{x \rightarrow 7}\frac{2 - \sqrt{x - 3}}{x^{2} - 49} is

A

29\frac{2}{9}

B

−249- \frac{2}{49}

C

156\frac{1}{56}

D

−156- \frac{1}{56}

Answer

−156- \frac{1}{56}

Explanation

Solution

Applying L-Hospital’s rule, lim⁡x→70−12x−32x\lim_{x \rightarrow 7}\frac{0 - \frac{1}{2\sqrt{x - 3}}}{2x}

=lim⁡x→7−14xx−3=−14.77−3=−156= \lim_{x \rightarrow 7}\frac{- 1}{4x\sqrt{x - 3}} = \frac{- 1}{4.7\sqrt{7 - 3}} = \frac{- 1}{56}.