1 I need to know the convergence of this series

2 I have to obtain the expression of dy/dx for the following function

3xy - 2x^2y + y^3 =0

3

The x radius is ?

Thanks

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- Sep 4th 2008, 10:51 AMkezmanCalculus questions
1 I need to know the convergence of this series

2 I have to obtain the expression of dy/dx for the following function

3xy - 2x^2y + y^3 =0

3

The x radius is ?

Thanks - Sep 4th 2008, 11:09 AM11rdc11
Use the integral test for the 1st problem to see if it converges

- Sep 4th 2008, 11:16 AMMoo
It's better to compare :

As n approaches infinity, 2k+5 ~ k and sqrt(3k²-1/2) ~ k^(3/2)

Therefore, (2k+5)/sqrt(3k²-1/2) ~ k/k^(3/2)=1/k^(1/2)

By comparison with the Riemann series, since 1/2<1, the series is not convergent.

Quote:

2 I have to obtain the expression of dy/dx for the following function

3xy - 2x^2y + y^3 =0

Quote:

3 5x^2 + 3y^2 = 16

The x radius is \sqrt{5} ?

Thanks

So transform it like it should be. - Sep 4th 2008, 11:27 AMkezman
on 2 ive got this

- Sep 4th 2008, 11:35 AMMoo
- Sep 4th 2008, 11:41 AMkezman
y^3 = y(2x^2 - 3x)

y^2 = x(2x -3) (is this legal?)

and then I derive the sqrt - Sep 4th 2008, 11:46 AMMoo