Answer to Question #236257 in Calculus for luka

Question #236257

Evaluate each of the following limits:

(a)lim √(x+2)-√(2-x)/x

x→0

(b)lim (2x+8/x^2-12)(1/x)/x+6

x→-6




1
Expert's answer
2021-09-20T17:39:46-0400

(a) "lim_{x\\to 0}\\frac{\\sqrt{x+2}-\\sqrt{2-x}}{x}=lim_{x\\to 0}\\frac{x+2-(2-x)}{(\\sqrt{x+2}+\\sqrt{2-x})x}=lim_{x\\to 0}\\frac{2}{\\sqrt{x+2}+\\sqrt{2-x}}=\\frac{\\sqrt{2}}{2}." .


(b) "lim_{x\\to -6}\\frac{\\frac{2x+8}{x^2-12}-\\frac{1}{x}}{x+6}=lim_{x\\to -6}\\frac{\\frac{(x+6)(x+2)}\n{x(x^2-12)}}{x+6}=lim_{x\\to -6}\\frac{x+2}{x(x^2-12)}=\\frac{1}{36}."


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