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Questions Asked

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

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

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

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