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Today, 11:53

Euge replied to a thread Ordering on the Set of Real Numbers ... Sohrab, Exercise 2.1.10 (b) ... in Analysis

The point was to use part (a) of your exercise, not the next exercise.

3 replies | 54 view(s)

Today, 00:59

Euge replied to a thread Ordering on the Set of Real Numbers ... Sohrab, Exercise 2.1.10 (b) ... in Analysis

Note $1^2 = 1$ and $1 \neq 0$.

3 replies | 54 view(s)

Today, 00:50

Euge replied to a thread Ordering on the Set of Real Numbers ... Sohrab, Exercise 2.1.10 (c) ... in Analysis

Hint: Proof by induction and part (b) of the exercise.

1 replies | 40 view(s)

August 17th, 2017, 06:02

Opalg replied to a thread Limits of Sequences ... Stoll Theorem 2.2.6 in Analysis

Yes! (Yes)

3 replies | 60 view(s)

August 17th, 2017, 02:10

MarkFL replied to a thread 231.12.3.65 Determine the smallest distance between a point and a line in Calculus

Small quibble...axis of symmetry is: t=-\frac{1}{105} So, since the parabola opens up, the vertex is a minimum, so the minimum distance will be...

8 replies | 155 view(s)

August 17th, 2017, 00:59

MarkFL replied to a thread 231.12.3.65 Determine the smallest distance between a point and a line in Calculus

For a parabola of the form: f(x)=ax^2+bx+c We know the axis of symmetry is at: x=-\frac{b}{2a} So, for:

8 replies | 155 view(s)

August 16th, 2017, 21:58

MarkFL replied to a thread 231.12.3.63 Determine the smallest distance between point and line in Calculus

Isn't this question a duplicate of the following? 231.12.3.65 Determine the smallest distance between a point and a line

1 replies | 37 view(s)

August 16th, 2017, 17:25

Jameson replied to a thread Statistics in Basic Probability and Statistics

Hey freedomdorm! I saw you posted this update on to another question so I gave you your own thread. Are you curious about the other question or do...

1 replies | 36 view(s)

August 15th, 2017, 23:46

Euge started a thread Problem of the Week #255 - Aug 15, 2017 in POTW for Graduate Students

Here is this week's POTW: ----- Let $\Bbb D$ be the open unit disc in the complex plane, and let $f$ be a continuous complex function on...

0 replies | 42 view(s)

August 15th, 2017, 23:19

Euge replied to a thread Problem of the Week #254 - Aug 01, 2017 in POTW for Graduate Students

No one answered this week's problem. You can read my solution below. For all $k \ge 1$, the $k$th tensor algebra of $\Bbb Z/n\Bbb Z$ is $(\Bbb...

1 replies | 83 view(s)

August 15th, 2017, 11:11

Opalg replied to a thread Limits of Sequences ... Sohrab Exercise 2.2.7 in Analysis

Edit. I wrote this before seeing Evgeny's comment above. You should probably look at both comments in parallel.] I think you are right. There is...

3 replies | 68 view(s)

August 15th, 2017, 08:55

Ackbach started a thread Problem of the Week # 276 - Aug 15, 2017 in POTW for University Students

Here is this week's POTW: ----- Can an arc of a parabola inside a circle of radius 1 have a length greater than 4? ----- Remember to read...

0 replies | 42 view(s)

August 15th, 2017, 08:54

Ackbach replied to a thread Problem of the Week # 275 - Aug 07, 2017 in POTW for University Students

Congratulations to Opalg for his correct solution to this week's POTW, which follows: Expand $(a+1)^n$ binomially to get $$a^{n+1} - (a+1)^n =...

1 replies | 85 view(s)

August 14th, 2017, 01:09

MarkFL replied to a thread Solar Eclipse 2017 in Chat Room

I was just reading about how tree leaves can form "pinhole cameras" and the eclipse can be seen in their shadows:

4 replies | 162 view(s)

August 13th, 2017, 14:03

MarkFL replied to a thread [SOLVED] 12 DeMoivre's theorem in Trigonometry

In case you're wondering how I obtained the following factorizations: 1+3i=(1+i)(2+i) 2-2i=-(1+i)^3 What I did for the first was to write: ...

13 replies | 237 view(s)

August 13th, 2017, 10:34

Jameson replied to a thread Probability of Event A then B in Basic Probability and Statistics

Hey RTCNC, I do agree that this question is similar to the one you asked yesterday, so for me that only highlights the fact that you should work...

3 replies | 79 view(s)

August 13th, 2017, 10:15

MarkFL replied to a thread [SOLVED] 12 DeMoivre's theorem in Trigonometry

What definition for "complex form" were you given? That was the confusing issue for me. I am aware of rectangular, polar and exponential forms for...

13 replies | 237 view(s)

August 13th, 2017, 06:27

Opalg replied to a thread Open and Closed Sets - Sohrab Exercise 2.4.4 - Part 3 in Analysis

The set $S = \{1/n:n\in\Bbb{N}\}$ is not open, because for example it contains the point $1$ but it does not contain any $\varepsilon$-neighbourhood...

2 replies | 54 view(s)

August 12th, 2017, 22:07

MarkFL replied to a thread [SOLVED] 12 DeMoivre's theorem in Trigonometry

I'm wondering if what we're supposed to do here is: 1+3i=(1+i)(2+i) 2-2i=-(1+i)^3 And so the product is: ...

13 replies | 237 view(s)

August 12th, 2017, 15:44

Jameson replied to a thread Probability of 2 Green Marbles in Basic Probability and Statistics

Well my questions still stand and I'm curious how you came up with this RTCNTC? :) There is a way to write the solution in terms of combinations,...

7 replies | 150 view(s)

August 12th, 2017, 12:09

anemone started a thread Problem of the week #275 Aug 12th, 2017 in POTW for Secondary School/High School Students

Here is this week's POTW: ----- Suppose \frac{3}{2}\le x \le 5. Prove that 2\sqrt{x+1}+\sqrt{2x-3}+\sqrt{15-3x}<2\sqrt{19}. ----- ...

0 replies | 64 view(s)

August 12th, 2017, 11:46

anemone replied to a thread Problem of the week #274 Aug 5th, 2017 in POTW for Secondary School/High School Students

Congratulations to lfdahl for his correct solution:), and you can find the suggested solution below: Note that $f$ is monotonically increasing and...

1 replies | 115 view(s)

August 12th, 2017, 10:38

Jameson replied to a thread Probability of 2 Green Marbles in Basic Probability and Statistics

Well often we see "combination" notation come up but it's important to think these problems through and not just use that. With probability type...

7 replies | 150 view(s)

August 12th, 2017, 08:03

Opalg replied to a thread Supremum Property (AoC) ... etc ... Yet a further question/Issue ... in Analysis

Yes. Sohrab is saying that if $\bigcap I_n$ consists of more than one point then it must contain two points, one of which is larger than the...

2 replies | 65 view(s)

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