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- Elementary functions. Calculating limits, derivatives and integrals. Optimization problems
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Jan16-12 Greg Bernhardt
Please post any and all homework or other textbook-style problems in one of the Homework & Coursework Questions...
Feb23-13 09:24 AM
1 45,340
Let f(x,y) = ( \frac{-y}{x^2 + y^2}, \frac{x}{x^2 + y^2}) with f : D \subset \mathbb{R}^2 \to \mathbb{R}^2 I...
Dec24-11 07:13 AM
3 1,224
What does this mean ! ?
Jul17-08 10:41 PM
2 1,551
Jan31-08 09:44 AM
1 3,825
Consider the heat equation in a radially symmetric sphere of radius unity: u_t = u_{rr}+{2 \over r}u_r \ for \ (r,t)...
Aug27-09 02:44 PM
1 638
Use the chain rule to show that dz/dx = (cos(theta) * dz/dr) - (1/r * sin(theta) dz/dtheta) and dz/dy =...
Sep8-13 03:59 AM
1 601
I define a consistent family, F, to be a set of intervals such that if I_1 and I_2 are in F then I_1 and I_2...
Feb28-08 08:11 PM
Pere Callahan
6 1,727
Is there a formula that will calculate time when I know the following...? Initial velocity = 0 Final velocity =...
Sep11-08 07:59 AM
3 1,676
If we parameterize the arc length of a vector valued function, say, r(s) and r(s) has constant curvature (not equal...
Mar21-10 11:29 PM
1 1,098
Find a number "k" such that exist only one intersection between the curve exponential k^x e and the straight xk. This...
Nov17-13 05:54 PM
5 540
My book (Saff&Snider) has the following theorem Suppose u(x,y) is a real-valued function defined in a domain D. If...
Jun14-09 09:33 PM
4 1,034
This is a question that came up in a conversation with my father who was a fighter pilot in ww2... we got to talking...
Mar6-10 01:20 PM
2 3,126
Hi everyone, I've been racking my brain about this problem, but can't seem to figure it out. It seems like it...
Jun11-13 07:49 PM
3 772
The first order KKT condition for constrained optimization requires that the gradient for the Lagrangian is equal to...
Apr12-12 02:56 PM
4 981
Hi, I want to know the solution of the following equation. a = argmin_{a} \\ where x_i, y_i are column vectors...
Apr15-11 05:29 AM
2 2,767
Hi, I need help with this problem; minimize x^3, subject to K= x-Ωπ so would the solution be K-Ωπ=x
Apr14-12 07:58 AM
1 988
I'm trying to find the regular parallelepiped with sides parallel to the coordinate axis inscribed in the ellipsoid...
Jul2-08 09:38 AM
1 1,213
I have the analytical first and second derivatives of a (multidimensional) lagrangian ( l = f - λh). X is the vector...
Jan21-12 05:04 PM
0 947
Construct a compact set of real numbers whose limit points form a countable set.
Oct8-04 09:35 AM
8 4,447
Suppose I'd like to construct a C^\infty generalization of a characteristic function, f(x): \mathbb R \to \mathbb R,...
Oct31-11 02:32 PM
Citan Uzuki
1 1,386
Today, I had the desire to construct a C^{\infty} approximation to a tent function. Specifically, for any positive...
Mar13-06 11:39 PM
5 1,654
How do you construct Peano curves? All pictures I have seen suggest that it is iterative process, however, I don't...
Sep22-08 05:50 PM
0 799
Hello--- I am reading a paper on numerical methods which requires a 2D function to be converted to a 1D function. ...
Mar2-10 09:43 AM
2 868
Can you prove that \mathbf{R} and \mathbf{R}-\mathbf{Q} have same cardinality? One way would be to say that...
Sep19-08 06:25 AM
3 1,798
This proof I think is related to our construction of R in class using equivalences classes of Cauchy sequences: Let...
Nov3-11 04:01 PM
3 1,080
I was looking at the construction of the real number system. I know dedekind cuts can be used(completely worthless...
Mar25-11 01:38 PM
16 2,807
Hi!!I am trying to construct in Matlab a C-infinity Odd Finction whose time derivative is always positive. The...
Oct23-06 08:22 PM
3 2,902
I have a question regarding this. I wish I were home right now so I can give the exact words. Anyways, the book...
Feb16-06 12:02 PM
7 1,830
Let be a differential equation : y^{(n)}=F(t,y,\dot y ,\ddot y , \dddot y,..........., y^{n-1}) then if we...
Jun10-06 05:54 AM
0 1,051
suppose i have a real function f=f(x) this function is smooth everywhere on the real line for example, f=e^x. ...
Mar19-10 08:22 AM
5 858
for any function f(x) how can you convert it to continued fractions in the form: ...
May18-07 08:58 AM
1 913
Does the continued product of fractions 1/2 x 2/3 x 3/4 x.....x (n-1)/n converge? If so, what does it converge to?
Apr5-09 08:58 PM
SW VandeCarr
4 1,293
I'm seeking a bit of affirmation or correction here before i try to solidify this to memory.... I know continuity...
Nov16-04 03:54 PM
6 10,599
How come sin(x^-1) is not continuous and xsin(x^-1) is?
Nov16-10 09:01 AM
12 6,093
X, Y metric spaces. f:X-->Y and X is compact. How do I prove that f is continuous if and only if G(f)={(x,f(x)):x in...
Oct29-08 07:30 PM
9 1,799
Consider f(x)=x^3-x^2+x+1 g(x)=\left\{\begin{array}{cc}{max\{f(t),0\leq t \leq x\}}\;\ 0\leq x \leq 1 \\ 3-x\;\...
Jan10-04 04:14 PM
1 1,975
My question is best stated by using an example: Suppose f is a function defined only for rational x, and for...
Sep30-09 09:37 AM
2 901
Can anyone help me with this problem? Say f(x) & g(x) are cont. at x=5. Also that f(5)=g(5)=8. If h(x)=f(x)...
Aug3-08 11:17 AM
7 1,468
I'm just wondering why in the definition of continuity, limit of function, or even just limit of a sequence, the...
Feb16-10 04:39 PM
2 1,101
Hello, I've allways wondered how to get to polar coordinates from cartisan coordinates. I took a course in fluid...
Feb21-13 04:35 PM
1 553
Just curious how to define continuity for mult dim. functions. I know that the topological and set theorectical...
Dec19-10 08:42 AM
5 3,640

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