Hi,(adsbygoogle = window.adsbygoogle || []).push({});

Suppose I have

[tex]\lim_{r\to 0} \left\{\int_0^{\pi} \frac{f(r,t)}{r^2}dt - \int_0^{\pi} \frac{g(r,t)}{r} dt\right\}[/tex]

and both integrals tend to infinity. So I combine them:

[tex]\lim_{r\to 0} \int_0^{\pi} \frac{f(r,t)-r g(r,t)}{r^2} dt[/tex]

now at this point, the numerator in the integrand does not go to zero as r goes to zero but rather [itex]\cos(t)[/itex] so it does go to zero at one point in the interval of integration. Can I apply L'Hospital's rule and conclude:

[tex]\lim_{r\to 0} \int_0^{\pi} \frac{f(r,t)-r g(r,t)}{r^2} dt\overset{?}{=}\lim_{r\to 0} \int_0^{\pi} \frac{\frac{d}{dr}\left[f(r,t)-r g(r,t)\right]}{\frac{d}{dr}r^2}dt[/tex]

Ok thanks,

Jack

**Physics Forums - The Fusion of Science and Community**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Can I apply L'Hopital's rule to this integral expression?

Loading...

Similar Threads - apply L'Hopital's rule | Date |
---|---|

I Do normal differentiation rules apply to vectors? | Apr 13, 2017 |

B Applying L'Hospital's rule to Integration as the limit of a sum | Mar 5, 2017 |

I Vector directions applied | Feb 9, 2017 |

I How do I apply Chain Rule to get the desired result? | Jan 15, 2017 |

When Can i apply L'Hopital's rule? | Oct 20, 2004 |

**Physics Forums - The Fusion of Science and Community**