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(a) [tex]lim_{n\rightarrow\infty}[/tex] ([tex]\sqrt{(n + a)(n + b)} - n)[/tex] where a, b > 0
(b)[tex]lim _{n\rightarrow\infty}[/tex] (n!)^{1/n2}
(b)[tex]lim _{n\rightarrow\infty}[/tex] (n!)^{1/n2}
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Rationalize the numerator by multiplying both numerator and denominator by [itex]\sqrt{n+ a)(n+b)}+ n[/itex]. Then divide both numerator and denominator by n.(a) [tex]lim_{n\rightarrow\infty}[/tex] ([tex]\sqrt{(n + a)(n + b)} - n)[/tex] where a, b > 0