# Science:Math Exam Resources/Courses/MATH103/April 2005/Question 05 (c)

MATH103 April 2005

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### Question 05 (c)

Consider the curve given by

${\displaystyle \displaystyle y=f(x)={\frac {1}{x^{p}}}}$

for ${\displaystyle \displaystyle 1\leq x\leq B}$ where ${\displaystyle \displaystyle p,B}$ are constants with ${\displaystyle \displaystyle B>1}$ and ${\displaystyle \displaystyle p>0}$.

Refer to parts (a) and (b) for the values of A (the area between the curve and the x-axis) and V (the volume obtained by rotating the curve about the x-axis).

(c) Now consider the limit as B tends to infinity. For what range of values of the constant p is it true that the volume V has a finite limit while the area A becomes infinite? Explain your answer in terms of your calculations from parts (a) and (b) using one sentence.

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