10.2 Detecting Convergence, Estimating Limits
Integrals of 1/x^p on intervals (0,1] and [1, inf)
This applet allows exploration of areas trapped between and the x-axis on the intervals (0,1] and [1,inf). The slider for p changes the exponent on x. The slider for r changes the lower limit of integration on an integral of f from x=r to x=1 by allowing . The slider for R changes the upper limit of integration on an integral of f from x=1 to x=R by allowing .
Question 1: What happens to each of these integrals when ?
Question 2: What happens to each of these integrals when ?
Question 3: What happens to each of these integrals when ?