Author Topic: most awesome question thread :) (Read 9154 times) Tweet Share

superflya · « **Reply #90 on:** February 25, 2010, 07:36:34 pm »

thanks so much

qshyrn · « **Reply #91 on:** February 25, 2010, 07:47:25 pm »

Quote from: moekamo on February 25, 2010, 07:28:09 pm

Quote from: superflya on February 25, 2010, 06:04:38 pm
the number of real solutions for $x^{4}-x^{3}=\csc ^{2}(x)-\cot ^{2}(x)$ is?

$x^{4}-x^{3}=\csc ^{2}(x)-\cot ^{2}(x)$
$\implies x^{4}-x^{3}=1$ (since $1+\cot^2x=\csc^2x \implies 1=\csc^2x - \cot^2x$ )

graphs the curves $y=x^{4}-x^{3}, y=1$ on calc and see how many intersections there are

well if ur gonna use the calc, you might as well use the solve function straight away and see how many ansewrs pop up (easier).
or u can do it in ur head by picturing y=x^4-x^3 = x^3(x-1) (quartic graphs look like a parabola and it passes 0 and 1) so when you draw a line y=1 , you can tell that it must cut 2 of the 'parabola arms'

superflya · « **Reply #92 on:** February 25, 2010, 07:58:57 pm »

yea just had a mindblank

tiredness isnt helping.

superflya · « **Reply #93 on:** July 04, 2010, 10:55:07 pm »

$\int \sqrt{\tan (x)}\ dx$

ishghwpao;hg;poahwhgw wtfffff?

fady_22 · « **Reply #94 on:** July 05, 2010, 11:44:55 am »

Quote from: superflya on July 04, 2010, 10:55:07 pm

$\int \sqrt{\tan (x)}\ dx$

ishghwpao;hg;poahwhgw wtfffff?

I doubt we'd be asked to evaluate that.
Unless it asks for the definite integral, which you can do on the calculator.

brightsky · « **Reply #95 on:** July 05, 2010, 05:25:13 pm »

Let $u = \sqrt{\tan(x)}$ , then $du = \frac{\sec^2(x)}{2 \sqrt{\tan(x)}} dx$

In terms of $u$ , this is:

$\frac{u^4 + 1}{2u}$

Hence,

$dx = \frac{2u}{u^4 + 1} du$

Substitute that back in:

$\int \sqrt{\tan(x)} dx = \int \frac{2u^2}{u^4 + 1} du$

Decompose it using partial fractions, should be a tad easier now.

superflya · « **Reply #96 on:** July 05, 2010, 07:07:54 pm »

this isnt a spesh question, found it and it looked interesting

gahh ive almost given up. ill try that brightsky

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