Calcus homework help because I'm too dumb to help my kid, please.

Discussion in 'General Discussion' started by digitalwanderer, Oct 8, 2019 at 8:54 PM.

  1. digitalwanderer

    digitalwanderer Dangerously Mirthful
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    upload_2019-10-8_14-49-33.png
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    She had some problems with her first calculus teacher about some things that the professor turned out to be VERY wrong about so she switched classes, is filing a complaint, and the department head is looking in to the matter. Purdue has been really good about it or I'd be raising holy hell, but they really do take care of their students. :)

    Any help is appreciated.
     

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  2. pcchen

    pcchen Moderator
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    For #1:

    Knowing that derivative of arctan(x) is 1/(1+x^2).

    let t = arctan(2x) so y = t^2, dy/dx = dy/dt * dt/dx = 2t * (arctan(2x))'
    let s = 2x so again (arctan(s))' = 1/(1+s^2) * 2
    so dy/dx = 2*arctan(2x) * 1/(1+4x^2) * 2 = 4 * arctan(2x) / (1+4x^2)


    For #2:

    (a) by "implicit differentiation" it means doing y' without solving y first
    so 9x^2-y^2=1 -> 2*9x - 2y * y'=0
    therefore y' = 18x/2y = 9x/y

    (b) solve y first:
    y^2 = 9x^2 - 1
    => y = +/- sqrt(9x^2 - 1), or (9x^2-1)^0.5
    therefore
    y' = +/- 0.5 * (9x^2-1)^(-0.5) * (9x^2-1)' = +/- 0.5 * (9x^2 - 1)^(-0.5) * 18x = +/- 9x/sqrt(9x^2-1)

    It can now be verified that y' is indeed 9x/y.
     
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  3. orangpelupa

    orangpelupa Elite Bug Hunter
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    Oh my poor brain
     
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  4. digitalwanderer

    digitalwanderer Dangerously Mirthful
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  5. iroboto

    iroboto Daft Funk
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    thanks man, this brings back memories
     
  6. maddy

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    thank you pcchen!! (im digi's daughter)

    i also um. just wanted to ask and see if this looks okay.
    20191009_145020.jpg

    am i doing these right? im struggling to be able to describe the true/false problems... especially because i dont feel confident in what im doing. the joys of transferring into a class that's way ahead of the one you were in...
     
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  7. pcchen

    pcchen Moderator
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    Glad that helped!

    For #1 I think you are doing great.

    #2 are all "prove or disprove this" questions and they can be quite annoying :)

    For (a):
    To explain it more rigorously, if f(x) is concave up for all x and f''(x) exists for all x, f''(x) > 0 for all x and vice versa. Therefore, if f(x) and g(x) are both concave up for all x, f''(x) > 0 and g''(x) > 0, so f''(x) + g''(x) > 0 for all x, therefore f(x)+g(x) is also concave up for all x.

    For (b): your counter example is good :) but it's not about the order of multiplication though, it's just that both (fg)' and f'g' are zero.

    For (c): it's actually not true because for example y = sin(x) + 100x also have y'''' = sin(x)

    For (d): to prove it more rigorously, mathematical induction should be used: if y = a^x then y' = ln(a) * a^x, so if nth derivative is (ln(a))^n * a^x, (n+1)th derivative is (ln(a))^n * ln(a) * a^x = (ln(a))^(n+1) * a^x, QED

    For #3 I think you missed a y' as (4y^3*y')' = 12y^2 * y' * y' + 4y^3 * y'', not 12y^2 * y' + 4y^3 * y''
    so it's y'' = (-12x^2-12y^2(y')^2)/(4y^3) = (-3x^2-3y^2(-x^3/y^3)^2)/(y^3) = (-3x^2-3y^2x^6/y^6)/(y^3) = (-3x^2-3x^4/y^4)/(y^3) = -3x^2(y^4 + x^4)/y^7
    and since x^4 + y^4 = 16, so it's -3x^2(16)/y^7 = -48x^2/y^7

    I guess it's common to not feel confident enough when doing mathematical proof though, even professional mathematicians make mistake in papers :)
     
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  8. orangpelupa

    orangpelupa Elite Bug Hunter
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    I leave this page open on my work computer when I leave it to got to the toilets or grab some food.

    Really good for making it looks like I'm working on something serious and complicated and not to be disturbed.

    (sorry, I can't help with anything, my brain instantly goes blank reading those numbers formula that looks as meaningful as hieroglyphs to me)
     
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  9. maddy

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    thank you. i really need the support and reassurance because... ow. and i'm pretty positive nobody at my house is able to help me because... yeah. calculus.

    this really helped me out though!! i went to my professor's office hours (first time i've done that in college :oops:) and since he just collected this he graded mine and i got a 48/50!! i went because another student asked him if they could do practice questions that modeled the ones that would be on our quiz today. between the two of us, i was the one who was understanding the concepts we were applying more :shock:

    i think i did well on it... it was open note and book, though, AND i spent too much time trying to understand how to use a program i put on my calculator last night to find the volume of a sphere, BUT i found it after 15 minutes or so...

    yea i hate these kind of questions

    this was the one he took two points off of because i didn't show the entire process of getting to the fourth derivative. but that's... that's whatever to me. i still got an a. he just wanted a little bit more.

    i think this is what genuinely helped the most. i had gone to my college's tutoring center for walk in tutoring to try and get this done (that's where i took the picture i posted) and the girl i talked to... i don't think she wasn't helpful, per say, but she's in higher level math courses and i could get forgetting what's taught in calc 1 when you've done multivariable calc. i've also just had a lot of trouble doing implicit differentiation and this helped me understand what the hell i'm supposed to be doing. although, i'm still getting used to reading and typing out math shit so i did have to google an ascii math converter to read this :p

    it's probably because i don't have a strong understanding of the subject yet, but some of the things you have to do to equations and numbers in calc seem impossible. it feels like fake math :???: but i'm working on it. it's cool as hell to me. i still can't believe i like math now but here we are :yep2:

    ANYWAYS. all that aside (can anyone tell that i'm my dad's kid by how much i write :oops:) thank you for your help. i never thought i'd be able to do calculus, yet alone really be in college. i know a lot of my confusion can stem from me just... not knowing some of the basics. like when we were still just doing limits and we were dealing with delta epsilon problems?? :| i honestly still don't get those. but i don't know how often they'll really come up, so i'm... not too worried about it right now.
     
  10. maddy

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    that's ok. i still sort of feel that way about it while i see them too. math is hard.
     
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  11. pcchen

    pcchen Moderator
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    Great to hear it helped! :)

    If what you are going to do is mostly on the practical side, I'd say don't worry too much about the delta epsilon things :) These are more about making rigorous proof and definitions. They are very important for mathematicians, but not really that important for real world applications. (and yes, there are real world applications of calculus! :) ) It's more important to understand the general idea of derivatives and integral (e.g. derivatives are rates of changing of a function, and integrals are the area surrounded by the function, etc.)
     
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  12. homerdog

    homerdog donator of the year
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    Oh I took calculus 1 and 2 in college, the hard versions for science and engineering students. Lemme help.

    Holy fuckin shit nevermind good luck.
     
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