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The Challenge of Mathematics
It is a privilege to have PHD student Lê Nguyên Hoang share his personal insights about the current state of Mathematics in an original guest post on my main website: Guest Post: The Challenge of Mathematics Hope it will set you thinking a little. Peace. -
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Mathematics: Post your doubts here!
You can refer to my supplementary site www.a-levelmaths.com (summaries handout section). I have written some stuff for the first 4 topics. Hope you will find it useful. Peace. -
Mathematics: Post your doubts here!
For the part where you mentioned x = a cos3 t, y = a sin3 t, is it x = a cos^3 t, y = a sin^3 t, or x = a cos(3 t) , y = a sin(3 t) ? -
Mathematics: Post your doubts here!
I am assuming (3/2-x) = 3/(2-x) and (4x/4+x^2) = 4x/ (4+x^2) Then ∫ (3/2-x)+(4x/4+x^2) dx = ∫ -(-3/2-x)+2*(2x/4+x^2) dx (shape the both parts of the integral in the format ∫ f '(x)/ f(x) dx, so that this can be reduced to ln |f(x)| ) = -3 ln |2-x| + 2 ln |4+x^2 | +C (shown)... -
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Mathematics: Post your doubts here!
(cosx+3sinx)^2 = cos ^2 (x) + 6 sinx cosx + 9 sin ^2 (x) = 0.5* [cos(2x)+1] + 3 (2 sinx cosx) + 9 * 0.5* [1-cos(2x)] (use the identities cos (2x) = 2 cos ^2 (x) -1 = 1- 2sin ^2 (x) for transformation)... -
Mathematics: Post your doubts here!
Here are the full workings: Hope this helps. Peace. -
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Mathematics: Post your doubts here!
There you go: Hope this helps. Peace. -
Mathematics: Post your doubts here!
This simply requires a tweaking of the double angel formula, where cos 2x = 2 cos^2 (x) -1 We rewrite things as cos 4x =2 cos^2 (2x) -1 ; making cos^2 (2x) the subject, we therefore have cos^2 (2x) = 1/2* (cos4x +1) (shown) Hope this helps. Peace. -
Mathematics: Post your doubts here!
Let X be the random variable denoting the height of a male student. Then X~N( 178, 5^2 =25) Let Y be the random variable denoting the height of a female student. Then Y~N( 168, 4^2 =16) Also, based on the above, we have Y-X~N( -10, 25+16=41) P( Y>X) =P(Y-X>0)=0.0592 (shown) Hope this... -
Mathematics: Post your doubts here!
x= cos^3 t ======> cos^2 t = x^ (2/3) ---------------(1) y= sin^3 t ======> sin^2 t = y^ (2/3) --------------(2) (1)+(2): x^(2/3) +y ^(2/3) =1 (shown) Hope this helps. Peace. -
Mathematics: Post your doubts here!
This is done implicitly. d/dx [ ln(xy)] = 1/(xy) * [ x (dy/dx) +y ] Hope this helps. Peace. -
Mathematics: Post your doubts here!
You simply take the exponential base on both sides. Hope this helps. Peace. -
Mathematics: Post your doubts here!
Posting the question paper would be nice, you know? -
Mathematics: Post your doubts here!
ln( 2+ e^-x )=2 2+e^-x = e^2 e^-x = e^2 - 2 -x = ln (e^2 - 2) Hence, x = - ln (e^2 - 2)= -1.68 (shown) Hope this helps. Peace. -
Mathematics: Post your doubts here!
Then yes, it would. Hope this helps. Peace. -
Mathematics: Post your doubts here!
You mean the derivative of the function?
