# Search results

1. ### Ideals in the ring Q[X]

Consider the ideal I of Q[x] generated by the two polynomials f = x^2+1 and g=x^6+x^3+x+1 a) find h in Q[x] such that I=<h> b) find two polynomials s, t in Q[x] such that h=sf+tg
2. ### Linear Algebra question: n x n determinants

Call the upper non-zero submatrix for U and the lower for L. Then the determinant is the product of their determinants, i.e det(U)det(L)
3. ### Normal Distribution

Why even use a binomial approximation? Let Y denote the number of computer chips whose lifetimes are less than 1.8*10^6. Then Y~Bin(100, 0.9082).
4. ### Parabolic cylindrical coordinates

Can someone, please, show me an example of when you are better of with parabolic cylindrical coordinates than with cartesian coordinates when computing a triple integral over a solid?
5. ### Confused on finding Eigenvalues and Eigenvectors

See http://mathworld.wolfram.com/CharacteristicEquation.html" [Broken].
6. ### Limit of Trig Function

scorpa, don't be so harsh on yourself. :wink:
7. ### Limit of Trig Function

\cos \left( {2x} \right) = \cos ^2 x - \sin ^2 x = (cos x - sin x)(cos x + sin x) does it ring a bell now? You have to do something with the numerator.
8. ### Partial integration help

How I started first? I tried with partial integration in many different ways.. :bugeye:
9. ### Partial integration help

How do I integrate: [tex]\frac{xarctan(x)}{(1+x^2)^2}[/itex]

Error vv
11. ### Calculating intercept with x-axis

Use the http://mathworld.wolfram.com/Mean-ValueTheorem.html" [Broken] on a)
12. ### Why is this limit of 2 variables undefined? it looks like both = 0!

To prove that lim f(x,y) does not exist, it suffices to show that the limit along one curve into (a,b) differs from the limit along a second curve. If lim f(x,y) does exist, however, then computing limits along individual curves will prove nothing (although, such computations will likely help to...
13. ### Why is this limit of 2 variables undefined? it looks like both = 0!

You can show that the limit is undefined by showing that the limit depends on how you approach zero. You can show that f(x,y) \longrightarrow \frac{1}{2} if you approach zero along the curve (\sqrt{y},y). So you have showed that the limit is both 0 and 1/2, i.e. it must be undefined.
14. ### Find instantaneous rate of change of 7/3z^2

Just http://mathworld.wolfram.com/Derivative.html" [Broken] it with respect to z.
15. ### What is the derivative of y=sin(x+y)?

The partial derivatives of f(x,y) = sin(x+y) are \frac{df}{dx} = cos(x+y) and \frac{df}{dy} = cos(x+y)
16. ### Lim f(0,y). y->0. L'H rule needed, did i do it right?

You seem to have misunderstood L'Hospitals rule. L'Hospitals rule states that \lim \frac{f(x)}{g(x)} = \lim \frac{f'(x)}{g'(x)} if \lim f(x) and \lim g(x) are both zero or ±\infty. L'Hospitals rule isn't necessary. Just use the standard limit for \frac{sin(x)}{x}
17. ### Linear Algebra Proof

Yes, you could say that. :smile:
18. ### Linear Algebra Proof

They are just using the assumption A = 2A^T in that step.
19. ### Linear Algebra - Basis

The general equation of a plane is Ax+By+Cz = D. D = 0 \Longleftrightarrow the plane goes through the origin.