The value of mathop {lim }limits_{x to 7} fra | vedclass

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(D) Applying $L$-Hospital's rule:$\mathop {\lim }\limits_{x 	o 7} \frac{{2 - \sqrt {x - 3} }}{{{x^2} - 49}}$$= \mathop {\lim }\limits_{x 	o 7} \frac

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$-\frac{1}{56}$

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(D) Applying $L$-Hospital's rule:$\mathop {\lim }\limits_{x 	o 7} \frac{{2 - \sqrt {x - 3} }}{{{x^2} - 49}}$$= \mathop {\lim }\limits_{x 	o 7} \frac{{\frac{d}{{dx}}(2 - \sqrt {x - 3} )}}{{\frac{d}{{dx}}({x^2} - 49)}}$$= \mathop {\lim }\limits_{x 	o 7} \frac{{0 - \frac{1}{{2\sqrt {x - 3} }}}}{{2x}}$$= \mathop {\lim }\limits_{x 	o 7} \frac{{ - 1}}{{4x\sqrt {x - 3} }}$$= \frac{{ - 1}}{{4(7)\sqrt {7 - 3} }} = \frac{{ - 1}}{{28\sqrt 4 }} = \frac{{ - 1}}{{28(2)}} = -\frac{1}{56}$.

The value of $\mathop {\lim }\limits_{x \to 7} \frac{{2 - \sqrt {x - 3} }}{{{x^2} - 49}}$ is

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