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 integration
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Jan
26
comment Contrapositive - Convergence of a sequence
@hardmath yes. it's hard to ask people to do something by themselves if there are others happy to offer the entire thing on a pretty platter :)
Jan
25
comment In how many ways can a $31$ member management be selected from $40$ men and $40$ women so that there is a majority of women?
strange. $\binom{40}{16} \cdot \binom{64}{15}$ sounds right to me
Jan
25
comment Given diagonals, lower base, and height, find the legs and upper base of isosceles trapezoid
are you looking for algebraic or geometric construction?
Jan
25
comment What substitution can work in $\int (x^2 \sqrt{x^2 + 1})e^{x (1 - \log{x})} dx$
perhaps you are expected to leave it in the integral form?
Jan
25
comment What substitution can work in $\int (x^2 \sqrt{x^2 + 1})e^{x (1 - \log{x})} dx$
It may be integrable, so the integral exists, but who says this has a nice closed form? You can always write it as a power series and integrate term by term...
Jan
25
comment What substitution can work in $\int (x^2 \sqrt{x^2 + 1})e^{x (1 - \log{x})} dx$
what makes you think there is an easy way to do this?
Jan
25
comment Given the time complexity, determine how many problem instances can be solved in one minute
@MortalMan see the second answer, he wrote out the whole thing...
Jan
22
comment Limit $\lim_{x \to 1} \frac{\log{x}}{x-1}$ without L'Hôpital
why is the last step obvious -- you have a 0/0 form?
Jan
22
comment Limit $\lim_{x \to 1} \frac{\log{x}}{x-1}$ without L'Hôpital
@hardmath you only need up to the quadratic term. The OP was not interested in minimizing the number of derivatives, just in avoiding to use L'Hospital's rule...
Jan
22
comment infinite sum of the sequences
@ClementC. makes sense, did not think about it
Jan
21
comment infinite sum of the sequences
@AndréNicolas how does it help? power of $t$ in $\cosh$ expansion coincides with the factorial term, here is it a half of that
Jan
21
comment Given the real number $t = - \frac 5 4 \pi$, give the values of the sine, cosine and tangent.
Since sine, cosine and tangent have the same values on each interval of length $2\pi$, finding these at $-5\pi/4$ is the same as at $-5\pi/4+2\pi = 3\pi/4$. Can you do this now?
Jan
19
comment Calculate the Integral $\int _0^{\frac{\pi }{2}}\:\frac{\sin^{7/2}x}{\sin^{7/2}x+\cos^{7/2}x}dx$
@Noam $$\frac{s}{s+c} + \frac{c}{s+c} = 1$$
Jan
19
comment Upper estimate of integral
edited to the best of ability, please double check
Jan
19
comment How to approximate linear relationship between two timeseries?
Could the one who downvoted please explain the downvote? The OP explicitly asked for a Excel/Matlab solution...
Jan
18
comment Can a function $f:[0,2\pi] \rightarrow 1$ have a PDF and CDF?
@StanShunpike not sure domain of what you are asking about. If domain of $f$ it wouldn't change much...
Jan
17
comment O(n) of given code
@user3904534 the intuition for what you were asking is simple. Note that $$\sum_{i=1}^n 1 = \Theta(n), \sum i = \Theta(n^2), \sum i^2 = \Theta(n^3) \ldots$$
Jan
17
comment O(n) of given code
@user3904534 it is irrelevant now, see the updated version.
Jan
17
comment Can a function $f:[0,2\pi] \rightarrow 1$ have a PDF and CDF?
@StanShunpike it means you cannot construct the CDF :), because $Y$ is not a valid random variable. You are right, if is was on any interval of length $1$, e.g. $[0,1]$ or possibly $[\pi, \pi+1]$, it would work just fine :).
Jan
6
comment Finding the no. of non-negative integral solutions to $x+y+2z=33$.
Yes, note that $(x,y,z) = (24.75,0,0)$ solves $x+y+z=24.75$ but not $x+y+2z=33$. Similarly, $(33,0,0)$ will solve the second one but not the first one. They have a different solution space.