Use Continuity to evaluate the limit, lim_x-4 5+root_x/root_5+x

Question

Use Continuity to evaluate the limit, lim_x->4 5+root_x/root_5+x

Suresh Chand · Accepted Answer

Solution: Given (lim_{x to 4} left ( frac{5 + sqrt{x}}{sqrt{5 + x}} right )) Clearly (sqrt{x}) is continuous for (x geq 0) and (sqrt{(5+x)}) is continuous for ((5 + x) geq 0 enspace Rightarrow enspace x geq -5) Therefore, (frac{5 + sqrt{x}}{sqrt{5 + x}})             ... (ii) is continuous for (x geq 0). So, Limit of (ii) exists. And, ( = lim_{x to 4} left ( frac{5 + sqrt{x}}{sqrt{5 + x}} right )) ( = frac{5 + sqrt{x}}{sqrt{5 + x}}) ( = frac{5 + 2}{3} = frac{7}{3})

Use Continuity to evaluate the limit, \(\lim_{x \to 4} \left ( \frac{5 + \sqrt{x}}{\sqrt{5 + x}} \right )\)

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Use Continuity to evaluate the limit, \(\lim_{x \to 4} \left ( \frac{5 + \sqrt{x}}{\sqrt{5 + x}} \right )\)

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