Hello iPod

Welcome to Math Help Forum! Quote:

Originally Posted by

**iPod** The variables t and x are related by t = x+√(x^2+2bx+c) where b and c are constants and

b^2<c. Show that

dx/dt=(t-x)/(t+b)

[CENTER]

$\displaystyle t = x+\sqrt{x^2+2bx+c}$

$\displaystyle \Rightarrow (t-x)^2 = x^2+2bx+c$

$\displaystyle \Rightarrow 2(t-x)\left(\frac{dt}{dx}-1\right)=2x+2b$

$\displaystyle \Rightarrow \frac{dt}{dx} = 1+\frac{x+b}{t-x}=\frac{t+b}{t-x}$

$\displaystyle \Rightarrow \frac{dx}{dt} =\frac{t-x}{t+b}$

Quote:

and hence integrate

1/√(x^2+2bx+c)

$\displaystyle t-x = \sqrt{x^2+2bx+c}$

$\displaystyle \Rightarrow \frac{dx}{dt}=\frac{\sqrt{x^2+2bx+c}}{t+b}$

$\displaystyle \Rightarrow \int \frac{1}{\sqrt{x^2+2bx+c}}\,dx=\int\frac{1}{(t+b)} \,dt $

$\displaystyle = \ln (t+b)+C$

$\displaystyle =\ln(b+x+\sqrt{x^2+2bx+c})+C$, provided $\displaystyle b+x+\sqrt{x^2+2bx+c}>0$

Can you finish up?

Grandad

PS Quote:

[and come someone tell me how to use the math symbols at this site.. i had to do everything in microsoft word ]

The language is called LaTeX, and you'll find some help on this site here: http://www.mathhelpforum.com/math-help/latex-help/

I also find the Wikipedia site helpful, here: LaTeX/Mathematics - Wikibooks, collection of open-content textbooks

When you've written some LaTex code, select what you've written and click the $\displaystyle \Sigma$ button on this editor's toolbar, and the editor will insert [tex]...[/tex] tags around the selection. Use 'Preview Changes' to check that it's OK.

To see any of the code I've used in my solution above, just click-left on any line and the code will appear in a separate pop-up window. Go on, try it now!

Grandad