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1 I need to know the convergence of this series
$\displaystyle \sum_{k=1}^{\infty} \frac{2k+5}{\sqrt{3{k^3} - 1/2}}$
2 I have to obtain the expression of dy/dx for the following function
3xy - 2x^2y + y^3 =0
3 $\displaystyle 5x^2 + 3y^2 = 16$
The x radius is $\displaystyle \sqrt{5}$ ?
Thanks
Use the integral test for the 1st problem to see if it converges
It's better to compare :Quote:
Originally Posted by 11rdc11
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.
Implicit differentiation, do you know it ?Quote:
2 I have to obtain the expression of dy/dx for the following function
3xy - 2x^2y + y^3 =0
This is the equation of an ellipse, which is x²/a² + y²/b² = 1Quote:
3 5x^2 + 3y^2 = 16
The x radius is \sqrt{5} ?
Thanks
So transform it like it should be.
on 2 ive got this
$\displaystyle dy/dx $ $\displaystyle = (2x^2 - 3x)/2y$
Hmmm I don't think you applied the chain rule properly ! o.OQuote:
Originally Posted by kezman
Would you mind showing your working ?
I get something like dy/dx=(4xy-3y)/(3x-2x²+3y²) (I did it quickly)
y^3 = y(2x^2 - 3x)
y^2 = x(2x -3) (is this legal?)
and then I derive the sqrt
This is the problem !Quote:
Originally Posted by kezman
The derivative of y^3 wrt x is 3y'y², by the chain rule. Remember, y is a function of x ! The RHS is weird too.
