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Questions Asked

frx:
Group Title
I have the function
\[f(x)=\frac{ \sin(x \pi ) }{ \sin(2x \pi) }\]
which is visually presented in the attached file.
…
 updated one year ago
 32 replies
 1 Medal
Mathematics

frx:
Group Title
1). \[\lim_{(x,y) \rightarrow (0,0)} \frac{ x ^{2}y ^{2} }{ x ^{4}+y ^{4} }\]
2). \[\lim_{(x,y) \rightarrow (0,0)} \frac{ x ^{2}y ^{2} }…
 updated one year ago
 10 replies
 No Medals Yet
Mathematics

frx:
Group Title
Show that the vectors (1,0,1,0,1,0) and (0,1,1,1,1,1) generate the same subspace in R^6 as the vectors (4,5,1,5,1,5) and (3,2,1,2,1,…
 updated one year ago
 No Medals Yet
Mathematics

frx:
Group Title
A particle moves around a circle x^2+y^2=25 at constant speed, making one revolution in 2 seconds. Find its acceleration when it is at (3,4)…
 updated one year ago
 5 replies
 1 Medal
Mathematics

frx:
Group Title
The vectors (1,2,3,4),(0,1,2,3),(0,0,1,2),(0,0,0,1) creates a basis in R^4. Decide the coordinates for the vector (1,1,1,1) in the given bas…
 updated one year ago
 16 replies
 2 Medals
Mathematics

frx:
Group Title
Are the following set of vectors in R^4 linearly independent?
\[\left\{ (1,0,2,1),(1,2,1,0),(1,1,0,1) \right\}\]
…
 updated one year ago
 12 replies
 1 Medal
Mathematics

frx:
Group Title
What is the shortest distance from the point (x,y,z) to (a) the xyplane (b) the xaxis?
Could someone please explain this one, maybe wi…
 updated one year ago
 11 replies
 2 Medals
Mathematics

frx:
Group Title
Have been looking for exercises similar to this one \[\int\limits_{}^{} \frac{ \sin2\theta }{ \cos ^{2}\theta+6\cos \theta+10 }d \theta \] …
 updated one year ago
 6 replies
 1 Medal
Mathematics

frx:
Group Title
I'm a bit confused. I thought I'd solved the problem but when running the integral through Wolframalpha the answer is totally different, am …
 updated one year ago
 12 replies
 1 Medal
Mathematics

frx:
Group Title
If a serie is convergent does it mean the serie can be rewritten as a taylor polynomial but it can't be rewritten if it's divergent? If not …
 updated one year ago
 1 reply
 No Medals Yet
Mathematics

frx:
Group Title
Is the serie \[\sum_{n=0}^{\infty} (1)^{n}\frac{ n+2 }{ 3^{n} }\]
convergent or divergent? Calculate is't value.
\[\lim_{n \rightarrow \i…
 updated one year ago
 11 replies
 2 Medals
Mathematics

frx:
Group Title
Show that \[e ^{x} \ge 1+x\] for all real numbers x
 updated one year ago
 13 replies
 1 Medal
Mathematics

frx:
Group Title
Let A be the matrix \[A=\left[\begin{matrix}1 & 2\\ 2 &4\end{matrix}\right]\] decide all the 2x2 matrices B such that AB=BA=0, where 0 is …
 updated one year ago
 20 replies
 1 Medal
Mathematics

frx:
Group Title
Question: For which real constants a and b does the vectors [(1,a,0),(a,1,1),(b,1,1)] lie in the same plane?
So know that the lines are …
 updated one year ago
 4 replies
 1 Medal
Mathematics

frx:
Group Title
The equation for an ellipse is \[\frac{ x ^{2} }{ a ^{2} }+\frac{ y ^{2} }{ b ^{2}}=1\] and the foci is given by (c,0) where \[c ^{2}=a ^{2}…
 updated one year ago
 13 replies
 1 Medal
Mathematics

frx:
Group Title
Show that if \[2^{m}+1\] is prime then
\[m=2^{n}\] \[n \in \mathbb{N} \]
Guidance: \[m=r*2^{n}\]
…
 updated one year ago
 25 replies
 1 Medal
Mathematics

frx:
Group Title
Proove that two Fermat numbers always are relatively prime. I have the lead that F_m  (F_n  2) for m<n.
 updated one year ago
 45 replies
 1 Medal
Mathematics

frx:
Group Title
I need help to proof that fermat numbers always are relatively prime. I've got the lead that \[F_{m}(F _{n}2), ...where... m<n\] and that…
 updated one year ago
 5 replies
 No Medals Yet
Mathematics

frx:
Group Title
Show that if r is a positive odd integer then the polynomial \[x ^{r}+1\] is dividable by \[x+1\]
 updated one year ago
 9 replies
 1 Medal
Mathematics

frx:
Group Title
For which values of the constant a does the equationsystem have infinty many solutions and then doesn't any solutions exist.
\[ax _{1} +(a…
 updated one year ago
 9 replies
 1 Medal
Mathematics

frx:
Group Title
For which value on the real constant a were the line L intersects the point (4,1,3), with the direction vector (3,a,2), the plane \[(x,y,z)=…
 updated one year ago
 12 replies
 2 Medals
Mathematics

frx:
Group Title
Show that the equation \[z ^{3}+(3+i)z^{2}+(63i)z+(68i)=0\] has a pure imaginary root and then solve the equation.
I know how to sol…
 updated one year ago
 7 replies
 2 Medals
Mathematics

frx:
Group Title
Let a>0
(a). Show using L'Hospitals rule that:
\[\lim_{x \rightarrow 0} x ^{a}\ln(x)=0\]
…
 updated one year ago
 46 replies
 2 Medals
Mathematics

frx:
Group Title
Show that \[x ^{2}+18\ln(x)+11>12x \] for x>1, I have no idea how to do the 18ln(x) messes things up for me...
 updated one year ago
 7 replies
 2 Medals
Mathematics

frx:
Group Title
Show that \[x ^{2}+18\ln(x)+11>12x \] for x>1, I have no idea how to do the 18ln(x) messes things up for me...
 updated one year ago
 3 replies
 No Medals Yet
Mathematics

frx:
Group Title
\[z ^{3}+2(1−6i)z ^{2}+2(1−12i)z−24i=0\]
\[−ib ^{3}−2(1−6i)b ^{2}+2(1−12i)bi−24i=0\]
\[−ib ^{3}−2b ^{2}+12ib ^{2}+2bi+24b−24i=0\]
…
 updated one year ago
 2 replies
 1 Medal
Mathematics

frx:
Group Title
How many words with 11 letters can you make with the letters in the following word:
COMBINATION
…
 updated one year ago
 13 replies
 1 Medal
Mathematics

frx:
Group Title
7x+18y=208
18=7(2)+4
7=4(1)+3…
 updated one year ago
 9 replies
 2 Medals
Mathematics

frx:
Group Title
Show, using L'Hopitals rule, that
\[\lim_{x \rightarrow 0} x^{a}lnx = 0\]
for a>0…
 updated one year ago
 5 replies
 1 Medal
Mathematics

frx:
Group Title
i. Altair
ii. Procyon
iii. Epsilon Indi
…
 updated one year ago
 3 replies
 1 Medal
Mathematics
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