Various questions on limits, derivatives and series

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Feb 12th 2009, 06:45 PM
Angel Rox

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Various questions on limits, derivatives and series

Plz help me with these questions... am really stuck in them ... and really need help urgently... I had to submit them in 2 hours... plz help..

Questions are in attached document... because i dunno how to type here in the forum... sorry..
Feb 12th 2009, 07:28 PM
Reckoner

1. Since the degree of the numerator exceeds the degree of the denominator, you should be able to tell that the limit is infinite. You can also see it by dividing the numerator and the denominator by $x^4$ , and noting that $\lim_{x\to\infty}\frac1x=0$ .

2. This should be easy. If you are having trouble, state where you need help.

3. This is a telescoping series: $\sum_{n=1}^\infty\ln\left(\frac n{n+1}\right) = \sum_{n=1}^\infty\left[\ln n - \ln(n+1)\right]$ .
Feb 12th 2009, 07:44 PM
Angel Rox

Thanx I am solving the questions right now... and I have done Q1 with your kind help

but in Q2 I really dont know from where should I start...first I thought of continuity but when I saw we have to show F'(x)=F1'(x)=f(x) I got confused... Plz kindly help me out that from where should i start...

and I am solving Q3 right now.. if i get any diificulty I'll write it here... Thanx...

but need help in Q2
Feb 12th 2009, 07:57 PM
Reckoner

Quote:

Originally Posted by Angel Rox

but in Q2 I really dont know from where should I start...first I thought of continuity but when I saw we have to show F'(x)=F1'(x)=f(x) I got confused... Plz kindly help me out that from where should i start...

You can differentiate $F$ and $F_1$ by differentiating each case separately. You should get $f(x)$ as the derivative. That's it.

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