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Aug
25
comment Where did I go wrong in my evaluation of the integral of cosine squared?
don't you need a trig substitution for that one :-)?
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
21
comment I need some help. Find $\int \frac{\sin^2 x \cos x}{\sin x+\cos x}$
Hi, welcome to Math.SE! Please update your question with some thoughts on the problem and we will be happy to guide you further.
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
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
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
comment Maximizing area under $y=e^{−{∣x∣}}$
see update to my answer from your (deleted) comment
Aug
19
comment Integrating $ \int_0^\infty \frac{x^5}{e^x+1} \, dx $
Nasty answer from WolframAlpha: wolframalpha.com/input/?i=integral+x%5E5%2F%28e%5Ex%2B1%29
Aug
19
comment How many ways can we arrange 7 books, including 2 math books and 1 physics book, with the math books next to each other and left of the physics book?
+1, clever to divide by 2 in the last case instead of specifying the cases
Aug
19
comment How many ways can we arrange 7 books, including 2 math books and 1 physics book, with the math books next to each other and left of the physics book?
@Thunder_Penguin yes, I think so
Aug
19
comment elimination method and solving for constants
yes see my answer below
Aug
19
comment elimination method and solving for constants
What is your question exactly?
Aug
18
comment In how many ways can 4 red, 3 blue and 2 green balls be arranged?
Welcome to Math.SE! What are your own thoughts on the problem? Please update your question with your ideas how to approach this task and we will be happy to guide you with hints
Aug
18
comment selection of balls of three colors with restrictions
both approaches seem correct to me
Aug
18
comment selection of balls of three colors with restrictions
for the actual number of solutions, look here math.stackexchange.com/questions/395022/…