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12h
comment The number of numbers lying between 1 and 200 which are divisible by either of 2 , 3 or 5?
Nice example of inclusion-exclusion
14h
comment Differential topology versus differential geometry
Try reading the introduction of this book, which I used as a graduate student: amazon.com/Differential-Topology-Graduate-Texts-Mathematics/dp/… (The introduction pages are available in the preview.)
14h
revised If a unit ball is compact then why a ball of radius 5 has to be compact too?
added 193 characters in body
15h
answered If a unit ball is compact then why a ball of radius 5 has to be compact too?
15h
comment Can This Expression Be Simplified? (Involves Square Roots)
Not really no. Although the terms $\beta = v/c$ and $\gamma = 1/\sqrt{1-v^2/c^2} = 1/\sqrt{1-\beta^2}$ are so commonly used in S.R., that you might want to use $\beta$ or $\gamma$ as abbreviations in your expression. E.g., $$\frac{4mltc^2(1-1/\gamma)}{1/\gamma} = 4mltc^2(\gamma - 1)$$
15h
answered Replacing occurrences of the same integer as follows: is it legitimate in subsequent steps of a proof?
18h
comment Find the range of this function
Hint: Rewrite your function as $2 + 10/(x^2 + 5)$. Now, what's the range of $1/(x^2 + 5)$?
1d
answered ODE boundary condition and integer values?
1d
comment Write $61.84 \times 10^{-3}$ in standard form
Standard form usually means $y \times 10^n$ where $y \in (-10,-1]\cup[1,10)$ and $n$ is an integer.
1d
comment If, $x+y=1, x^2+y^2=2$ Find $x^7+y^7=??$
Explaining a joke spoils it, but here it is: Germane in this context means "relevant, pertinent". DB's inclusion of the value of $u_{70}$ was not germane. And I take it you were toying with that idea with your $u_{125}$, which I rewrote as $u_{5^3}$ to create the illusion that $125$ expressed as $5^3$ explained its importance (which it doesn't, because it doesn't have any!).
1d
comment If, $x+y=1, x^2+y^2=2$ Find $x^7+y^7=??$
+1 Excellent. $u_{5^3}$ is completely germane, probably even more so than $u_{70}$.
2d
comment Why associativity $h \circ (g \circ f) = (h \circ g) \circ f$ is required in composition?
To make sure that the action is well defined. If this equality did not hold, the order in which we acted with those functions would matter and that would make arbitrary compositions problematic.
Jul
2
comment Linear dependence of these functions?
Yes. For a $n \times n$ square matrix $M$, $\det M \neq 0 \Leftrightarrow \ker M = \{ 0 \} \Leftrightarrow nullity(M) = 0 \Leftrightarrow rank(M) = n$.
Jul
2
revised Linear dependence of these functions?
added 15 characters in body
Jul
2
answered Linear dependence of these functions?
Jul
2
comment Why is $\max(x, x')$ equivalent to $\frac{1}{2}( x + x' + |x - x' |)$?
There's an easy proof. Consider three cases: $x > x', x = x', x < x'$.
Jul
2
answered What does $A^{B}$ mean?
Jul
2
comment Proof inequality using Lagrange Multipliers
@Macavity, your equations aren't right. What Amad27 has written is. While I agree on the solution (with $\lambda = 4$), after playing with it for 15 minutes it's not clear to me how to deduce it from these equations. Amad27, do you have to use Lagrange multipliers? If not, I'd refer you to the other answer.
Jul
2
comment About Laplace transform, how to solve it
Sounds like you need to go back to some Laplace transform basics. Try this great lecture from MIT: ocw.mit.edu/courses/mathematics/…
Jul
1
comment Proof inequality using Lagrange Multipliers
$\nabla f = (\partial f/\partial a, \partial f/\partial b, \partial f/\partial c)$, similarly for $\nabla g$. The equation $\nabla f - \lambda \nabla g = 0$ is the Lagrange equation.