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Homework Help: I have math exam tomorrow and i need some help.

  1. Jun 23, 2005 #1

    GrP

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    excuse me for my bad english, but i'm trying hard.

    1. function f(x), for x>0 is defined with:

    f(x)=(x^4)^(x^2)

    ^ - potency

    find stationary points of the function f(x) on the interval (0,infinite).

    what exactly do i do here?
    do i use logarithm on both sides, and then i get:

    log(y)=(x^2)*log(x^4)

    and then i different (differential) both sides, and set y'=0
    and i calculate x?
    is this right so far?

    now i want to get local min. and max.
    and i different again, and then what?
    and i need to find out if these points are globlal min and max.


    2. integral from 1 to infinity (((x^2+1)^(1/2))/((x^3)*(x^2-1)^(1/2)))dx

    and ideas what could i do? what would "u" be? (u^2)=(x^2)+1?

    please help me asap
    thank you!
     
  2. jcsd
  3. Jun 23, 2005 #2
    1. Thats right so far.
    2.

    [tex] \int_1^{\infty} \frac{\sqrt{x^2+1}}{x^3\sqrt{x^2-1}}dx [/tex]

    Well first off, you'll need to do an improper integral.

    First thing I would try is a trig substitution, then maybe look at it by parts if that doesn't work. u = x^2 might get you somewhere but I don't know.
     
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