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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- September 4th 2008, 11:51 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 - September 4th 2008, 12:09 PM11rdc11
Use the integral test for the 1st problem to see if it converges

- September 4th 2008, 12:16 PMMoo
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. - September 4th 2008, 12:27 PMkezman
on 2 ive got this

- September 4th 2008, 12:35 PMMoo
- September 4th 2008, 12:41 PMkezman
y^3 = y(2x^2 - 3x)

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

and then I derive the sqrt - September 4th 2008, 12:46 PMMoo