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Math Help - a few limits

  1. #1
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    a few limits

    1) lim (5-sqrt[4+3x]) / (7-x), x going toward 7

    2) lim (tan9x) / (1-cos7x), x going toward 0

    3) lim (5sqrt[x]-2) / (x-32), x going toward 32, and the 5 is part of the radical so i guess its x^(1/5)
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  2. #2
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    anyone?
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  3. #3
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    Hello,
    Quote Originally Posted by Shadowfox1 View Post
    1) lim (5-sqrt[4+3x]) / (7-x), x going toward 7
    \lim_{x \to 7} ~ \frac{5-\sqrt{4+3x}}{7-x}

    Multiply by \frac{5+\sqrt{4+3x}}{5+\sqrt{4+3x}}

    then use identity (a-b)(a+b)=a^2-b^2 to simplify the top =)

    2) lim (tan9x) / (1-cos7x), x going toward 0
    \lim_{x \to 0} ~ \frac{\tan (9x)}{1-\cos(7x)}=\lim_{x \to 0} ~ \frac{\tan(9x)}{x} \cdot \frac{x}{1-\cos(7x)}=\lim_{x \to 0} ~ 9 \cdot \frac{\tan(9x)}{9x} \times \frac 17 \cdot \frac{7x}{1-\cos(7x)}

    These should be known limits :/


    3) lim (5sqrt[x]-2) / (x-32), x going toward 32, and the 5 is part of the radical so i guess its x^(1/5)
    \lim_{x \to 32} ~ \frac{\sqrt[5]{x}-2}{x-32}

    You can note that x-32=(\sqrt[5]{x})^5-2^5
    And in general, a^k - b^k = (a-b)(a^{k-1}+a^{k-2}b+a^{k-3}b^2 + ... +b^{k-1})
    (here is what I've done about this formula : http://www.mathhelpforum.com/math-he...484-k-b-k.html)
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