(Apologies for the lack of LaTeX formatting - I usually do my typesetting with MathType, but I only have Microsoft Equation Editor on this computer which doesn't have LaTeX export).
This isn't a homework question, but is problem I've discovered I'm facing after diving into another problem, but...
I'm writing a program that generates every possible valid Mastermind code.
That itself is easy. There are 6 colors in 4 possible positions. Cycling through them all is done like so:
for(int i = 0 to 1295 ) { // 1295 == 6^4 - 1, there are 1296 possible permutations of colors
color1 = (...
Ah, how careless of me.
And we're done:
\displaylines{
I = \int {\sin \left( {2x} \right)\cos \left( x \right)} dx \cr
\sin \left( {2x} \right) = 2\sin \left( x \right)\cos \left( x \right) \cr
I = \int {2\sin \left( x \right)\cos ^2 \left( x \right)dx} \cr
u = \cos...
Thanks all.
This does my working look alright?
\displaylines{
I = \int {\sin \left( {2x} \right)\cos \left( x \right)} dx \cr
\sin \left( {2x} \right) = 2\sin \left( x \right)\cos \left( x \right) \cr
I' = 2\sin \left( x \right)\cos ^2 \left( x \right) \cr
u = \cos \left(...
[SOLVED] Some antiderivatives
I've got a few antiderivatives to find, I've found most of them and they check out fine with my CAS, but three of them I'm having difficulties with.
The first:
Homework Statement
I = \int {{{\sec ^2 \left( x \right)} \over {\left( {1 + \tan \left( x \right)}...
Indeed, that solved it. Thank you.
I have one more question to ask:
I need to show that:
{\mathop{\rm Artanh}\nolimits} \left( {{\mathop{\rm Sin}\nolimits} \left( {{\textstyle{\pi \over 4}}} \right)} \right) = {\mathop{\rm Ln}\nolimits} \left( {1 + \sqrt 2 } \right)
Here's my working so...
The original question was "Find x, using the definitions of the hyperbolics in terms of exponentials"
...from this expression:
2 = {\mathop{\rm Cosech}\nolimits} \left( x \right) - 2{\mathop{\rm Coth}\nolimits} \left( x \right)
Here's my working so far, reducing down to the final polynomial...
[SOLVED] 3rd degree exponential polynomial
Homework Statement
Derived from the original question:
"Reduce to find x"
2e^{3x} - e^{2x} - 2e^x = 1
The Attempt at a Solution
Inspection fails, since the answer is transcendental. I have the answer from my CAS, but I can't figure...
Ah, that solves it then. Thanks.
As an aside, how can I make this:
{{dy} \over {dx}} = {{2y - x^2 } \over {y^2 - 2x}}
into this:
{{dy} \over {dx}} = {{x^2 -2y } \over {2x - y^2}}
They're meant to be identical, but I can't think how.
Thanks!