# Problem in understanding calculating limit.

• Aug 13th 2010, 02:26 AM
Real9999
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
• Aug 13th 2010, 04:03 AM
HallsofIvy
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.
• Aug 13th 2010, 04:24 AM
Real9999
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!
• Aug 13th 2010, 04:28 AM
Real9999
This forum is so awesome! And I will certainly donate to this forum as soon as I get my new bank card !!!