# Thread: Problem in understanding calculating limit.

1. ## 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

2. 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.

3. 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!

4. This forum is so awesome! And I will certainly donate to this forum as soon as I get my new bank card !!!