how would i find something like:
max[\frac{x}{2} + cos(x)] where x\epsilon [0,\pi] and ...
max[\frac{x}{2} + cos(x)] where x\epsilon [-\pi,0]
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here's what i did for max[\frac{x}{2} + cos(x)] where x\epsilon [0,\pi]:
first we need critical...
im actually getting the hang of it now. but stuck on dot product of cross products..
e.g. show... (AXB) . (CXD) = (A.C)(B.D) - (A.D)(B.C)
here's what i have done but its partially correct.
(AXB)i = \varepsilon_{ijk}A_jB_k.
(CXD)i = \varepsilon_{ijk}C_jD_k
so (AXB) . (CXD) =...
hi peeps. just a quick one.
(a) how would you go around working out the Fourier for exponential functions..
simply something like e^x? (b) and how can this be applied to work out Fourier series for cosh and sinh (considering cosh = e^x + e^-x / 2) etc etc..
first of all.. is e^x even or...
i was attempting to cancel everything out at the end without considering obvious facts in the beginning but i guess that would be a mistake..
for the right hand limit:
\lim_{h\to 0+} \frac{f(0+h)-f(0)}{h} = \lim_{h\to 0+} \frac{{\sin \frac{1}{0+h}}-f(0)}{h} = \lim_{h\to 0+} \frac{{\sin...
thnx for all the advice.. I've done some research on this and I've just still got a bit of problem here...
i want to prove that sin(1/x) is not differentiable by using the LIMITS method..
[SIZE="3"]ive worked this out so far:
the left hand limit and right hand limits need to be proved...
thanks a lot for that. it does help but there is far too much information there. i was just looking for a general explanation of the fundamentals and how the notations can be used to solve questions such as proving that:
grad(A.B) = (B.Delta)A + (A.Delta)B + BX(CurlA) + AX(CurlB)
etc etc...
Hi there is there a tutorial or post explaining vector calculus subscript notation please?
e.g. Eijk Kklm
dil djm etc etc
is there a tutorial explaining these thoroughly and how these can convert into div grad and curl??
i've used the search engine but can't seem to find them. thnx
the function is definitely sin(1/x) and NOT x.sin(1/x)
so basically am i right in assuming that to answer a question like this (show its not differentiable at 0), i have to first show that its discontinuous at 0 and deduce that since its discontinuous at 0 then it can't be differentiable at 0...
a function is differentiable if [ f(x) - f(xo) / (x - x0) ]
exists
i can appreciate i have to do this.. but how would i show that this derivative doesn't exist at 0... n wuld it be continuous at that point or not?but from here
Hi there just a general question: this involves continuity and differentiability
suppose:
f(x) = sin 1/x if x not equal to 0
f(0) = 0
PROVE F IS NOT DIFFERENTIABLE AT 0
i understand if it is not differentiable at 0 then it may not be continuous at 0. however is there...