using the equation ##u(x,y)=f(x)g(y)##, first, I substitute the value of ##u_{xx}## and ##u_{yy}## in the given PDE. after that solve the ODEs but I can't understand about the ##u_{t}##.In my solution, I put ##u_{t}=0## because u is only the function of x and y. Is it the right approach, to me...
Lemma
Let f be a bounded function on [a,b]. If P & Q are partitions of [a,b] and P ##\subseteq## Q , then
L(f,P) ##\leq## L(f,Q) ##\leq## U(f,Q) ##\leq## U(f,P) .
Question is "How can P have bigger upper darboux sum than Q while it is a subset of Q"
I think it is "True" because the hypothesis is true and the conclusion is False.
:cry::cry:But in the answer sheet, the answer is " This is False. The hypothesis is true, but the conclusion is false:## -1^2=-1## , not1."
Firstly I converted the given equation to a quadratic equation which is
##z^2- (\sqrt3)z+1=0##
I got two solutions:
1st sol ##z=\frac {(\sqrt3 + i)} {2}##
2nd sol ## z=\frac {(\sqrt3 -1)} {2}##
Then I found modulus and argument for both solution . Modulus=1 Arguments are ##\frac...
I only know about the meridians, Meridians are the imaginary lines that connect the north pole to the south pole.
360degree=60*360 minutes=21600 minutes.