# Search results

1. ### Function Continuity Proof in Real Analysis

##c = sup \{x \in [a, b]: f(x) \le 0 \}## f(c) < 0 c ∈ [a, b] a≤c≤b a≤x≤b c ≥ x x≤c≤b f(b)>0 b∉S Intuitively it makes so much sense and I feel really close but it hasn't clicked yet
2. ### Function Continuity Proof in Real Analysis

I see the logic of the first statements, here's my attempt There is also a possibility that there are several c's for which f(c) = 0 correct? But we are trying to show if there is at least one. If ##f(c) < 0##, then it's in an interval (a,c] I am thinking this is where p comes in and there is...
3. ### Function Continuity Proof in Real Analysis

I can't figure out the rest of it either The hint says show f(c) = 0 by contradiction and consider two cases. Apply the fact that if f is continuous at 'a', ∃ an open interval I centered at 'a' such that f(x) >0for all x ∈ I. Explain why 'c' not equal to 'a' which will mean a<c. Then let 'p' be...
4. ### Function Continuity Proof in Real Analysis

Thank you so much, Can't believe it was right there and I couldn't see it. So for showing a ≤ c from the set def we know that a≤x≤b and as c in an upper bound it's c ≥ x and by transitivity a ≤ a Now on to the rest of this problem :)
5. ### Function Continuity Proof in Real Analysis

Homework Statement We've been given a set of hints to solve the problem below and I'm stuck on one of them Let f:[a,b]->R , prove, using the hints below, that if f is continuous and if f(a) < 0 < f(b), then there exists a c ∈ (a,b) such that f(c) = 0 Hint let set S = {x∈[a,b]:f(x)≤0} let c =...
6. ### Proof about limit superior

for a large enough n, wouldn't ##M_n## = s? a > s a + s > s + s = 2s (a+s)/2 > s so s < u I'm still trying to see the next part
7. ### Proof about limit superior

Homework Statement 2. Relevant equation Below is the definition of the limit superior The Attempt at a Solution I tried to start by considering two cases, case 1 in which the sequence does not converge and case 2 in which the sequence converges and got stuck with the second case. I know...
8. ### Python Python 3.0 , encoding="utf-8" for encryption

I had recently upgraded my version of python from 2 to 3. I had a program that encrypted a text file by converting a character to its Unicode value, altering it and then changing it back to a character using the ord() and chr() methods. This does not seem to work with python 3 and I was...
9. ### Angle relationships of a blazed diffraction grating

These look really helpful I will have a look into them. I had been reading that the Littrow configuration you mentioned had high efficiency. However wouldn't the order with the most energy be reflected back on the incidence beam and due to the conservation of energy the other orders be less intense?
10. ### Angle relationships of a blazed diffraction grating

On another note, I'm likely to make this another thread but my aim is to uses the grating to combine two laser beams of different wavelengths. I want to do this in an energy efficient manner. Do you know any good resources I could use that explains the math of a blazed grating well?
11. ### Angle relationships of a blazed diffraction grating

Thank you, this makes perfect sense now!
12. ### Angle relationships of a blazed diffraction grating

I am trying to understand how a blazed diffraction grating works and came across a deduction I don't understand. I believe that you don't need to know much about optics to answer this question as it is more geometry related. I have the diagram below of a diffraction grating with all the relevant...
13. ### Error propagation when dividing by exact number

Yes, I can get the error from the spectrophotometric measurement which is ±0.0005 from the readings which is around 0.09% for my first reading and 0.48% for my last. So I don't need to bother with calculating the error in the concentration. Got it thanks :)
14. ### Error propagation when dividing by exact number

Homework Statement Some Background - We are calculating the amount of acetylsalicylic acid in a sample using spectrophotometry. We were told to make sure to include the error in our answer. So first to calculate the moles of acetylsalicylic acid in a measured mass. 0.1620 ± 0.0005g measured...
15. ### Damped oscillation and time between displacement maximums

Oh I see. The period is, ##\dfrac{2\pi}{\omega}##, which means that the equation becomes zero at this period meaning that the peaks occur at this period which is independent of ##\varphi##. Thank you all.
16. ### Damped oscillation and time between displacement maximums

I tried to take what both of you said into account and it seemed to work. I was able to solve for t but it is not what I expected as is seems to still depend on the dampening constant ##\Upsilon##. Did I make a mistake somewhere?
17. ### Damped oscillation and time between displacement maximums

My attempt at a solution did not show up. Here it is
18. ### Damped oscillation and time between displacement maximums

Homework Statement [/B] Question 3.9 Homework Equations equation for dampened ocillation[/B] The Attempt at a Solution In case this might appear confusing, I derived(with respect to t) the equation for dampened oscillation given above and tried to solve for when it equaled zero...
19. ### Underground living: Which project idea is better?

Cities need to become larger as more people want to live there. Building down will provide that space while being less obstructive. There could be added benefits that would lower the cost of living by saving energy. A heating and cooling system may not be needed because the ground will provide...
20. ### Underground living: Which project idea is better?

Thanks for your reply, I personally liked the first one as well.
21. ### Underground living: Which project idea is better?

True will definitely consider that, I was just worried our scope would become to big. Can you tell me which idea you would prefer to see in a project @sankonpure6.
22. ### Underground living: Which project idea is better?

Hello, Physics forum community.I have a project for an intro to engineering class in which I must design a system to solve an environmental problem. This class is only an introduction so I'm not sure how detailed and specific our work has to be. I must have been feeling very sci-fi at the time...
23. ### Effect of mass on skid distance of car experiment

Thank you so much for your replies I found them extremely helpful. I didn't know about axle friction @rcgldr and that link you sent was very helpful @haruspex.
24. ### Effect of mass on skid distance of car experiment

interesting, so when the load increases the surface of the rubber changes making it more slippery? that makes sense. Our track was a kind of metal and the wheels were a hard plastic. Is it safe to say these materials do not have an interesting property like rubber?
25. ### Effect of mass on skid distance of car experiment

Firstly, thank you so much for your reply. here's a little sketch of our spring launcher system before the spring had been compressed at all. We can alter how much it's bee compressed(x) by moving the second purple block back and forth. so in our first test with just the cart we compressed the...
26. ### Effect of mass on skid distance of car experiment

Homework Statement I know this is long, but that is only because this question requires me to be thorough, conceptually I think it isn't difficult. To make it easier to read I bolded the important parts. In Physics lab, we were told to conduct an experiment to investigate the effect off mass...
27. ### Using Kirchoff's laws to find current in complex circuit

Homework Statement Homework Equations V=IR and kirchoff's laws The Attempt at a Solution Number three is my attempt at finding a solution but I got stuck when I had to find an expression for loop one on the diagram. Thanks in advance for your help...

Thank you
29. ### Two point charges and electric potential difference

Homework Statement In an experiment modeling point charges I had to find equipotential lines. I did so using a voltmeter. The results looked like this: Not a good quality picture, but the equipotential line on the right says 1.3 mV and the one on the left says 2.3mV. From this I had to...
30. ### Integrating this function

1. Homework Statement I'm trying to integrate this, the only variable is y the others(x,w) are all constants. Homework Equations The ways of integrating that I am familiar with are substitution, trigonometric substitution, by parts & partial fraction decomposition. The Attempt at a Solution...