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Math Help - Problem in understanding calculating limit.

  1. #1
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    Problem in understanding calculating limit.

    I have a problem in calculating the limit for an equation.

    The equation is \frac {Aap^a+Bbp^b}{Ap^a +Bp^b}, where A, B, a, b are positive constants, with a > b.

    I am required to explain what happens to the value of the above equation when p approaches 0, and when p approaches infinity.

    The answer given in the textbook is when p approaches 0 the value of the equation approaches b and when p approaches infinity the value of the equation approaches a.

    Can someone explain in detail how to get to the above answers? Thank you very much in advance XD
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  2. #2
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    To take the limit as p goes to 0, divide both numerator and denominator by the smallest power of p.

    Here, that gives \frac{Aap^{a-b}+ Bb}{Ap^{a-p}+ B}. Because a- p is positive, as p goes to 0, p^{a- b} goes to 0.

    To take the limit a p goes to infinity, divide both numerator and denominator by the largest power of p.

    Here, that gives \frac{Aa+ Bbp^{b-a}}{A+ Bp^{b- a}}. Because b- a is negative, as p goes to infinity, [tex]p^{b- a} goes to 0.
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  3. #3
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    Oh yeah!, it has become brutally clear now! and I think that is Ap^a-b + B in the first denominator, right?

    Thank you so much for your help!
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  4. #4
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    This forum is so awesome! And I will certainly donate to this forum as soon as I get my new bank card !!!
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