$Q1)\lim_{x\to5}\frac{4-\sqrt{21-x}}{\sqrt[3]{x-13}+2}$
$Q2)\lim_{x\to\frac{4}{3}}\frac{6x^{2}-5x-4}{3x^{2}+17x-28}$
$Q3)\lim_{n\to\infty }\frac{(n+1)!-(n-1)!}{(n+1)!+(n-1)!}$
$Q1)\lim_{x\to5}\frac{4-\sqrt{21-x}}{\sqrt[3]{x-13}+2}$
$Q2)\lim_{x\to\frac{4}{3}}\frac{6x^{2}-5x-4}{3x^{2}+17x-28}$
$Q3)\lim_{n\to\infty }\frac{(n+1)!-(n-1)!}{(n+1)!+(n-1)!}$
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$Q1)\lim_{x\to5}\frac{4-\sqrt{21-x}}{\sqrt[3]{x-13}+2}$
$=\lim_{x\to5}\frac{4-\sqrt{21-x}}{\sqrt[3]{x-13}+2}.\frac{4+\sqrt{21-x}}{(\sqrt[3]{x-13})^{2}-2\sqrt[3]{x-13}+4}.\frac{(\sqrt[3]{x-13})^{2}-2\sqrt[3]{x-13}+4}{4+\sqrt{21-x}}$
$=\lim_{x\to5}\frac{16-21+x}{x-13+8}.\frac{(\sqrt[3]{x-13})^{2}-2\sqrt[3]{x-13}+4}{4+\sqrt{21-x}}$
$=\lim_{x\to5}\frac{x-5}{x-5}.\frac{(\sqrt[3]{x-13})^{2}-2\sqrt[3]{x-13}+4}{4+\sqrt{21-x}}$
$=\frac{3}{2}$
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$Q4)\lim_{x\to0}\frac{2^{3x}-3^{5x}}{sin(7x)-(2x)}$
$Q5)\lim_{n\to\infty }(\frac{2n^{2}+n+5}{2n^{2}+n+4})^{3n^{2}+1}$
$Q6)\lim_{n\to\infty }\frac{n\sqrt[3]{3n^{2}}+\sqrt[4]{4n^{8}+1}}{(n+\sqrt{n})\sqrt{7-n+n^{2}}}$
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[IMG]$\huge 4-{\color{Magenta} \lim_{x\rightarrow 0}(\frac{2^{3x}-3^{ax}}{sin7x-2x})}=\lim_{x\rightarrow 0}(\frac{\frac{8^{x}-243^{x}}{x}}{\frac{sin7x-2x}{x}})=\frac{ln8-ln243}{a}$ [/IMG]
Q6)
\[\lim_{n\rightarrow \infty }\frac{n\sqrt[3]{3n^2}+\sqrt[4]{4n^8+1}}{(n+\sqrt{n}+\sqrt{7-n+n^2})}\\=\lim_{n\rightarrow \infty }\frac{n^\frac{5}{3}\sqrt[3]{3}+n^1\sqrt[4]{4+\frac{1}{n^8}}}{n^2(1+\frac{1}{n})\sqrt{\frac{7 }{n^2}-\frac{1}{n}+1}}=\sqrt{2}\]
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[URL="http://alnasiry.net/forums"][IMG]http://alnasiry.net/forums/uploaded/2_iraqiflag.gif[/IMG][/URL]
$Q7)\lim_{n\to\infty }\frac{n^{3}}{1^{2}+2^{2}+3^{2}+...+n^{2}}$
$Q8)\lim_{n\to\infty }\frac{3n^{2}+2}{1+2+3+...+n}$
$Q9)\lim_{n\to\infty }\frac{(n+1)!-n!}{3(n^{2}+1)(n-1)!}$
$Q10)\lim_{x\to 0}\frac{x^{3}-3x^{2}}{\sqrt[3]{x^{2}+8}-2}$
; 06-06-2016 03:59 PM
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; 06-05-2016 08:23 AM
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