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Math Help - Limits

  1. #1
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    Limits

    lim x tending to infinity ((2-x)^40*(4+x)^5)/(2-x)^45
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  2. #2
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    Quote Originally Posted by prasum View Post
    lim x tending to infinity ((2-x)^40*(4+x)^5)/(2-x)^45
    HINT: \frac{{\left( {2 - x} \right)^{40} \left( {4 + x} \right)^5 }}{{\left( {2 - x} \right)^{45} }} = \left( {\frac{{4 + x}}{{2 - x}}} \right)^5
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  3. #3
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    Quote Originally Posted by prasum View Post
    lim x tending to infinity ((2-x)^40*(4+x)^5)/(2-x)^45
    Do you mean

    \lim_{x \to \infty} \frac{(2-x)^{40}(4+x)^5}{(2-x)^{45}}

    ? There's a language for that.
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  4. #4
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    i am sorry in the numerator it is (2+x)^45
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  5. #5
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    Much the same. IF you were to multiply everything out, the numerator would be x^{45} (NOT -x^45) plus terms involving lower powers of x and the denominator would be -x^{45} plus terms involving lower powers of x.

    General rule: If a rational function has polynomials of the same degree in numerator and denominator, the limit,as x goes infinity, is the ratio of those leading coefficients. If the numerator has lower degree than the denominator, the imit, as x goes to infinity, is 0. If the numerator has higher degree than the denominator, the limit, as x goes to infinity, does not exist.
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