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9h
comment Prove that $a+\frac{1}{b}>2$ or $b+\frac{1}{a}>2$ for two strict positive numbers
Nice way, simpler than mine.
9h
revised Prove that $a+\frac{1}{b}>2$ or $b+\frac{1}{a}>2$ for two strict positive numbers
[Edit removed during grace period]
9h
answered Prove that $a+\frac{1}{b}>2$ or $b+\frac{1}{a}>2$ for two strict positive numbers
10h
comment Common tangent line to two functions
You are welcome. Two answers have already been given, one of which has the same calculation. There is no need of another!
10h
comment Common tangent line to two functions
I am minus sign error prone, yes, those are the values. Will delete comment with switched around signs so it will not confuse others.
10h
comment Common tangent line to two functions
And yes, the common tangent line joins the points of tangency. So it has slope equal to the slope you computed earlier, $2a$ or equivalently $-2b-2$.
10h
comment Common tangent line to two functions
Almost finished. The slope $m$ you wrote down is equal to $2a$. That gives a reasonably nice equation. Substitute $b=-a-1$ and solve the resulting quadratic.
11h
comment Distribution of distinct object problem
It is the same idea. The number of ways is the number of $10$-letter "words" over the alphabet A, B, C where there are $5$ A's, $2$ B's, and $3$ C's. We can choose where the A's go in $\binom{10}{5}$ ways, and so on.
11h
comment Finite abelian group as Z-module
Look at the integers modulo $5$, under addition. How would we define $(1/5)a$?
12h
comment Distance between a point $X$ and a line $2x-y = 1$
Maybe they wanted you to say $\frac{|2x-y-1|}{\sqrt{5}}=10$! As to your question about "which one" it would be wrong to pick out one.
12h
comment Distance between a point $X$ and a line $2x-y = 1$
The displayed formula is a Cartesian equation that does the job. Alternately we could write it as $500=(2x-y-1)^2$. That would be more Cartesian, in the sense that the absolute value function cam after Descartes.
13h
comment why are the Bisection and Newton Method for finding roots complementary to each other?
They form a nice hunting team, one slow and steady, the other awfully quick but distractable. But once Bisection puts her on the right track, Newton usually can be counted on to finish things quickly.
13h
comment Solve the equation $7t+[2t] =52 $ ,where $[x]$ denotes the floor function for $x$.
The beginning was good. From what you wrote you can conclude that $t=n+\frac{k}{7}$ for some integer $n$ and some integer $k$ between $0$ and $6$. Then the end should come quickly.
13h
comment Property of a sequence being an enumeration of the rationals.
I think that for any specific $x$ it can be either. What do you mean by "is it possible to find out"?
20h
comment Calculation of area in 2 definite integrals given function $y=x^2$
As you saw, the pink area is always twice the blue. The only way they can be equal is if the the areas are both $0$.
20h
comment Calculation of area in 2 definite integrals given function $y=x^2$
The calculation looks fine.
22h
comment Product of two transcendental numbers is transcendental
For 3), $e$ and $\ln 2$ are transcendental (the latter by Lindemann-Weierstrass), but $e^{\ln 2}$ is not.
23h
revised To find a field of $p^{2}$ elements ,where $p$ is prime
added 21 characters in body
23h
answered To find a field of $p^{2}$ elements ,where $p$ is prime
23h
comment Limit of a function of multiple variables: $\lim_{(x,y) \to 0}\dfrac{x^2y}{17x^2+y^2}$
The proof shows it exists. For (after the cancellation of $r^2$ that OP did) we have an expression whose top has absolute value $\le r$, however $\theta$ varies, and yes, $\theta$ can vary, and whose bottom is $\ge1$, again whatever $\theta$ might be.