• Support PF! Buy your school textbooks, materials and every day products via PF Here!

I have math exam tomorrow and i need some help.

  • Thread starter GrP
  • Start date


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

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


^ - 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:


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!
1. Thats right so far.

[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.

Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving