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  1. Top | #1

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    $Q1)\lim_{x\to5}\frac{4-\sqrt{21-x}}{\sqrt[3]{x-13}+2}$

    $Q2)\lim_{x\to\frac{4}{3}}\frac{6x^{2}-5x-4}{3x^{2}+17x-28}$

    $Q3)\lim_{n\to\infty }\frac{(n+1)!-(n-1)!}{(n+1)!+(n-1)!}$

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  3. Top | #2

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  5. Top | #3

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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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  7. Top | #4

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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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  9. Top | #5

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  11. Top | #6

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  13. Top | #7

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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]

  14. Top | #8

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    . .

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  16. Top | #9

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    Q6)
    \[\lim_{n\rightarrow \infty }\frac{n\sqrt[3]{3n^2}+\sqrt[4]{4n^8+1}}{(n+\sqrt{n}+\sqrt{7-n+n^2})}\\=\lim_{n\rightarrow \infty }\frac{n^\frac{5}{3}\sqrt[3]{3}+n^1\sqrt[4]{4+\frac{1}{n^8}}}{n^2(1+\frac{1}{n})\sqrt{\frac{7 }{n^2}-\frac{1}{n}+1}}=\sqrt{2}\]


    : n ( )2 1
    [URL="http://alnasiry.net/forums"][IMG]http://alnasiry.net/forums/uploaded/2_iraqiflag.gif[/IMG][/URL]


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  18. Top | #10

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    $Q7)\lim_{n\to\infty }\frac{n^{3}}{1^{2}+2^{2}+3^{2}+...+n^{2}}$

    $Q8)\lim_{n\to\infty }\frac{3n^{2}+2}{1+2+3+...+n}$

    $Q9)\lim_{n\to\infty }\frac{(n+1)!-n!}{3(n^{2}+1)(n-1)!}$

    $Q10)\lim_{x\to 0}\frac{x^{3}-3x^{2}}{\sqrt[3]{x^{2}+8}-2}$
    ; 06-06-2016 03:59 PM

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  20. Top | #11

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    ; 06-05-2016 08:23 AM

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  22. Top | #12

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