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Aug
25
comment Where did I go wrong in my evaluation of the integral of cosine squared?
@JoeTaxpayer not sure, still thinking. This way is quick and elegant - one step takes care of the integration
Aug
25
answered Where did I go wrong in my evaluation of the integral of cosine squared?
Aug
25
revised Where did I go wrong in my evaluation of the integral of cosine squared?
added 25 characters in body
Aug
23
revised If $f’(x) = \sin x + (\sin4x)(\cos x)$, then $f’(2x^2 + \pi/2) $is?
added 25 characters in body; edited title
Aug
23
reviewed Approve If $f’(x) = \sin x + (\sin4x)(\cos x)$, then $f’(2x^2 + \pi/2) $is?
Aug
23
revised General question on Taylor Series
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Aug
23
answered General question on Taylor Series
Aug
19
comment Proof: A matrix with $m$ rows and $n$ colums has $nm$ entries.
@user50224 they are axiomatic definitions of what matrix is. See Pedro Tamaroff's question in the top of your queue
Aug
19
comment Proof: A matrix with $m$ rows and $n$ colums has $nm$ entries.
@user50224 These should be axiomatic
Aug
19
comment Polynomial must be monotone between its extrema
@takecare yes, something like that
Aug
19
comment Polynomial must be monotone between its extrema
@takecare part got erased...
Aug
19
comment limit with greatest integer function
So what do you think is $$\lim_{x \to -7} \frac{[x]+7}{x+7}?$$
Aug
19
revised limit with greatest integer function
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Aug
19
answered Proof: A matrix with $m$ rows and $n$ colums has $nm$ entries.
Aug
19
comment Polynomial must be monotone between its extrema
@takecare think about how you got there -- you must have $f'<0$ on the left and $f'>0$ on the right, or vice versa, so the point has to be an extremum -- otherwise you have $f'$ with the same sign on both sides, like $f(x) = x^3$ at $x=0$, which means the function is monotonic there
Aug
19
reviewed Approve Method of moment estimator. Deconvolution
Aug
19
comment Polynomial must be monotone between its extrema
@takecare we assumed $f$ is not monotonic on $(a,b)$, which means it must be sometimes increasing ($f'>0$) and sometimes decreasing ($f'<0$), which means by IVT there is a point in $(a,b)$ where $f'=0$ and there $f$ is neither increasing nor decreasing.
Aug
19
comment Polynomial must be monotone between its extrema
@takecare think of Intermediate Value Theorem applied to $f'$ - it cannot be negative and positive without being 0 somewhere as well. The case of $f'(x) = 0 = f''(x)$ is a situation where you have a zero derivative, but it does not happen at an extreme point of $f$ -- this is only possible if it is a critical point...
Aug
19
answered Lagrange's multiplier method find the highest and the lowest point
Aug
19
revised Lagrange's multiplier method find the highest and the lowest point
edited tags