hELp me /b how i solve this without l hopital rule?
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hELp me /b how i solve this without l hopital rule?
come here asians i have fresh math for you guys!
what the fuck is sen
sen = sine , cos = cosine
>>677283246
sen?
What are you trying to solve? It clearly says the limit is 2.
>>677283246
cos^2 (x) = 1 - sin^2(x)
simplify
1+sin^2(x)
applyin x gives 2
>>677283990
Why doesn't it just say "sin"like every other textbook?
>>677283246
Extremity direction existence as dashwoods do up. Securing marianne led welcomed offended but offering six raptures. Conveying concluded newspaper rapturous oh at. Two indeed suffer saw beyond far former mrs remain. Occasional continuing possession we insensible an sentiments as is. Law but reasonably motionless principles she. Has six worse downs far blush rooms above stood.
>>677284830
Did you just like hit random words on your phone as it suggested it to you?
>>677283246
Any time you have a sine term in the denominator and are dealing with limits that will reduce the denominator to zero, you have to look at the top term and see if it will also reduce to zero at that point. Naturally, 0/0 is not the answer. You should remember a familiar limit that says x/sinx as x approaches 0 = 1. You have to apply the same principle here
>>677284407
That will just yield (1-sin^2(x))/(1-sin(x))
>>677284407
how you turn 1- sin^2(x) into 1 + sin^(x)? what changed the negative to positive?
Is anyone in this thread capable of helping me with sequences and series?
cos^2(x)=1-sin^2(x)=(1-sin(x))*(1+sin(x))
The whole shit becomes 1+sin(x) and you apply the pi/2 ezpz
>>677285463
What about them?
>>677285250
(1-sin^2(x))/(1-sin(x)) = sin(x)+1
>>677285374
he didn't do that
>>677285574
Im fucking lost with this shit. Half the time I don't even know where to begin or what the difference is between finding convergnece or the sum.
Sup can u also help me on this one? Thanks
OP 1-sin^2(x) factors to be (1+sinx) and (1-sinx)
>>677285839
Too broad. Give me some example to work with
>>677286043
>>677286043
>>677286276
Use the ratio test and then once you have it simplified plug in the condition. I.E. For the ratio test r<1. So solve for r an d then do that condition and you'll find one of the border values for the interval of convergence.
>>677286723
How do Ik to do the ratio test homie?
>>677286809
Wait, how did you get to radius of convergence before ratio test?
You're supposed to learn the divergence, integral, limit, power, and ratio test before you do anything with interval/radius of convergence. You need to know those methods before moving forward.
>>677286723
Nvm bro so the interval or radius is the number I find when I do the ratio test?
>>677287038
Ik bits and bits like I knew the ratio test I just dont know when to use this shit
>>677287068
No. The rario test doesn't yield a number, it yields an expression. Once you have the expression you can solve for x and you'll get an interval of some sort.
>>677287133
You should try to learn it concretely, otherwise you'll keep hitting road bumps on the road to the next level.
After this you'll probably move into Taylor Polynomials, and you'll be lost if you don't grasp the concept of series and their convergence.
>>677287287
Taylor I tried to learn. I have a test tomorrow on this shit and rn I'm doing a review. I'm probably fucked but it's an online class so I might be able to cheat. I plan to pretty much learn all this again after I get the test out of the way
>>677285945
With or without using l'hopital
>>677287485
>I plan to pretty much learn all this again after I get the test out of the way
Be careful, there's always going to be new things to learn, and you can sometimes lull yourself into a false sense of security.
Calculus can be extremely easy if you understand all of the concepts and methods, and be painfully slow if you're bullshitting your way through.
A problem that would take you five minutes will take you 15 if you don't understand it. It doesn't matter if the test is online or not, you need to at least understand how to solve for it.
>>677287790
Well the notes with the class are fucking terrible and tbh I've procrastinated a shit ton but like even then pauls online calc notes, khan academy, and patrick jmt have enormous amounts of videos on the subject (because it seems like a big topic) but we had barely any time to cover it in class.
>>677287943
Believe it or not, reading through your textbook is faster and more efficient than videos. If you really get stuck check them out, but what would take five minutes of reading will turn into 20 minutes of watching a video
>>677287943
Hey man, sometimes you have to deal with an ass Professor and just read the text on your own. Last year I took Calc. II and Prob. & Statistics with an ass Professor and I just had to deal with the book more.
You have to learn the material any way you can. Don't procrastinate either, because that will only make the mountain of shit even larger.
>>677287748
without l hopital
>>677285945
1 - 2cos(2x) = 1 - 2(1 - 2sin^2(x)) = 4sin^2(x) - 1 = (2sin(x) - 1)*(2sin(x) + 1).
So the ratio is
1 - 2cos(2x)/1-2sin(x) = -(2sinx +1)
Evaluate it at x = pi/6 to get -2
>>677288517
Listen, if you need to do these sort of limits without using l'hospital, then you essentially need to cancel the term in the denominator which causes it to go to zero. Most of the cases, this just involves factoring the numerator to get the denominator(or a factor in the Denom which is causing the problem), like I did in >>677288621
Hope this helps
>>677284777
Because Christians.
Can't have 'sin' in class. That leads to pregnancy.
>>677288403
I'm a high school senior this is AP calc BC online. Probably gonna take the class again in college just to make sure I have it all down. This year I just havent really cared at all like I'm taking AP chem as well. 1st semester of that we had a teacher that didn't teach us any AP material at all, held our hand the entire way. 2nd semester we currently have a brand new teacher, fresh out of college... can't teach for shit and all we've learned is very inconsistent like we can't really apply the knowledge to a problem if given
>>677288917
Fair enough man. I was pretty incompetent in HighSchool. I couldn't study to save my life. If you cant jump to Calculus I in college, then just make sure you take your time and learn the material thoroughly. Calculus is extremely important as it forms the basis for most Science and Math classes.
Don't fuck around. If you choose to, you could be a young Newton.
cos^2(x)=1-sin^2(x)
1-sin^2(x)=1^2-sin^2(x)=(1-sin(x))(1+sin(x))
(1-sin(x))(1+sin(x))/(1-isn(x))=1+sin(x)
lim(x->pi/2) 1+sin(x)=2
>>677288621
how cos(2x) = 1- 2sin^2(x)?
>>677289960
It's a standard identity.
cos(2x) = cos^2(x) - sin^2(x) = 1 - 2sin^2(x) = 2cos^2(x) - 1
Does any of this help? It's just using the identity that cos^2(x) + sin^2(x) = 1.
>>677289960
Its an identity. Its equivalent to that and 2cos^2(x) -1 .
>>677290182
>>677289960
You should really review trig functions. You could blast through this in 20 minutes if you understood the methods of simplification. You should be happy that you're given examples, but you should at least understand how others got to their conclusion/solution.
>>677290182
there is any explanation how 2 comes in front of sin or should i just memorize this?
>>677290816
If you want to fall into an hour tizzy you can look at proofs, or you can memorize it. Formulas/identities have proofs/explanations but I don't know about you but I prefer to use the method first and then maybe look at the proof.
Either way you'll probably have to memorize it for application use.
>>677290816
Don't actively try to memorize this, anon.
Ok, what's the definiton of double angles that you use?
Is it sin(2x) = 2sin(x)cos(x) and cos(2x) = cos^2(x) - sin^2(x)?
If so, you can derive the identity I used by using the second one listed above and the identity that sin^2 + cos^2 = 1(this one is a very important one - just remember it always).
This will directly give you 1 - 2sin^2(x) = cos(2x).
Tell me if you use some other defn, and I'll tell you how to derive it from that.
As to the memorization part, I remember these since I used them a lot during HS and maybe freshman year in college - but initially, I used to take a few seconds to derive them myself.
>>677290816
Same guy >>677291177
Again, I don't recommend memorization because there are a CRAZY amount of identities, especially when you get to triple angles, and half angles. Instead it's better to remember a few base ones and derive the ones you need.
>>677289376
Hey if you're still here I was trying to solve a of the problem I posted and I don't know what to do with the x
>>677290816
>>677290816
cos(2x) = cos^2(x) - sin^2(x) (from the angle addition formula)
cos^2(x) - sin^2(x) = (1 - sin^2(x)) - sin^2(x) (from the identity 1 = cos^2(x) + sin^2(x))
(1 - sin^2(x)) - sin^2(x)=1 - 2sin^2(x)
alternatively
cos^2(x) - sin^2(x) =cos^2(x) - (1 - cos^2(x)) (from the identity 1 = cos^2(x) + sin^2(x))
cos^2(x) - (1 - cos^2(x))=2cos(x) - 1
>>677291825
ill take a look m8
bump
>>677292860
What are you bumping for?
OP's problem is solved
cos2=1_sin2=(1-sin)(1+sin)
cos2/'1-sin) = 1+sin
Im looking Khan academy videos right now to see all trig identities + proofs , if you guys know any other good channels to learn thanks
>>677292942
I want to help that guy with the ratio test.
>>677293175
Anon, you need videos when something has to be explained. This is just pure mathematics, all are logical and you'd same waaay more time by consulting a textbook, or just googling for identities.
>>677293228
Alright anon
>>677283246
>Expand it as a taylor series
>Evaluate
>Bound it
>Use squeeze theorem
>>677291825
Solved it, will post in a second.
>>677295228
Have to justify the interval real quick m8
>>677291825
>>677295228
Oh ok the x is just pulled out. Do you have a steam or something I can add you on man? I might need some help with the taylor shit later if you're willing
Have a look at this:
http://www.arndt-bruenner.de/mathe/Allgemein/trigsimpl.htm
>>677295228
I really appreciate this /b/ro
>>677295705
Just post a thread on /sci/. I or other Anons will help out. Its not like /b/ where threads die quickly it'll be up there for some time.
For this I was able to show the integral test(could have also used the limit comparison test), but I'm assuming and hoping you know the alternating series test.
It converges conditionally, but not absolutely. Which is enough to include -1 as a point of convergence.
You can also use symbolab to check your answer. I don't know if they used the same method as me, but the answer is the same result.
>>677295228
The second one the limit is zero and I have pulled out 1/(x-2). Do I just substitute 1/(x-2) for r?
>>677296834
Why did you have to do the integral test and why did you leave out the x^n in the numerator. The alt. series test... I'm so confused
>>677297238
Well, if your Teacher doesn't care about inclusive or exclusive intervals: E.G. (-1,1) or [-1,1] then focus on the first page, if he does care you have to prove that 1 or -1 is included or excluded.
>>677297584
>>677297238
You essentially have to prove if the endpoints are also convergent or divergent. That problem is one relatively easy problem, finding the general interval, and then two subproblems, testing both interval endpoints.
>>677297584
I think we do I just kinda remembered it a different way. Can you just explain why in the integral test you used 1/(3n+1) instead of the original problem? Same with the alt series test you used (-1)^n/3n+1
>>677297991
Substitute the endpoint values for x.
x=1 and then x=-1
>>677298103
Oh shit I get it now. Did you have to use the integral test?
>>677298278
Integral test, or limit comparison test, or limit test.
Integral test seemed the easiest to me.
>>677298628
Ok bro thank you so much. So you go on /sci/? I'll probably be back in here in like 7 or 8 hours asking for help.
>>677298724
If I'm home I'll look out for it m8. Taylor series are a little more straightforward, although it does require some techniques/methods to simplify certain series.
It shouldn't be too bad as long as you know derivatives well.
>>677298872
Yeah I got calc 1 down derivative/integrals are easy as hell. This shit... this shit is just wierd. Like is there any fucking use with sequences/series?
>>677298872
>>677298724
Forgot the link for symbolab. Its a good calculator and explains the logic behind the steps.
https://www.symbolab.com/solver/series-calculator/%5Csum_%7Bn%3D0%7D%5E%7B%5Cinfty%7D%20%5Cleft(%5Cfrac%7Bx%5E%7Bn%7D%7D%7B3n%2B1%7D%5Cright)/?origin=button
>>677283246
Solving the equation won't help you get pussy.
>>677299104
For certain problems you need to use a series to simplify it. When working with complex functions, you use power series to separate imaginary components from real components. You can also use them to estimate/approximate values.
Probably what you'll be doing next is creating series out of functions and maybe using them to make approximations of values.
The idea is that you're taking abstractions and turning them into polynomials, which are easy to deal with.
>>677299342
But it will help you become enlightened. You wish you were popping like Newton.
