A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • 4 years ago

Can anyone help me with a notation question? In Problem Set 1, 1G-5 part b, there is (n over 1) etc with no division line, it's been a long time since I took Calculus in the first place and I can't recall what the significance is? When I look at the answers I'm getting it seems like it should just be n, but their solution for y to (p+q) power throws me for a loop. Any help would be appreciated. Thanks!

  • This Question is Closed
  1. anonymous
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Do you have a link to the problem set or can you post the problem?

  2. anonymous
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    I assume, this is the link... http://ocw.mit.edu/courses/mathematics/18-01-single-variable-calculus-fall-2006/assignments/

  3. anonymous
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    I didn't find the problem...please post.

  4. anonymous
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    http://ocw.mit.edu/courses/mathematics/18-01sc-single-variable-calculus-fall-2010/part-a-definition-and-basic-rules/problem-set-1/ It's on page 7 of the Differentation pdf

  5. anonymous
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    \[y ^{n}=u ^{n}v + \left(\begin{matrix}n \\ 1\end{matrix}\right) u ^{n-1}v ^{1} + \left(\begin{matrix}n \\ 2\end{matrix}\right) u ^{n-2} v ^{2} + ... + uv^{n}\] now that I've worked out the equation editor on here, thats the equation I was referring to.

  6. anonymous
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    The part in parentheses is referring to combinations. The whole form is referring to the binomial theorem. Pascal's triangle will also help with this form. Here is a quick link to help with basic examples. http://regentsprep.org/Regents/math/algtrig/ATP4/bintheorem.htm I'll look at your specific problem and get back to you.

  7. anonymous
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    okay...first look for a pattern... take p=1 and q=1 and find the (p+q)derivative or 2nd derivative ...=2 then take p=2 and q= 1 and find the (p+q)derivative or 3rd derivative...=6 note that when n=2 , solution is 2 or 2*1 note that when n=3 , solution is 6 or 3*2*1 therefore make the jump that the solution will be n! (n p)(x^p*(1+x)^q)....=n! Here is another way to think about it.... . For example y=x^2(x+1)^2=x^2(x^2+2x+1)=x^4+2x^3+x^2 Lets take the fourth derivative (the sum of the exponents) y'=4x^3+6x^2+2x y"=12x^2+12x+2 y"'=24x+12 +0 y4=24+0+0=24 note that we multiplied 4*3*2*1=4! in our leading term.... That's all that is happening in the problem....everything else is going to zero... I hope this helps....

  8. anonymous
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Okay, but I'm just wondering what that specific notation of the \[\left(\begin{matrix}n \\ 2\end{matrix}\right)\] or \[\left(\begin{matrix}n \\ p\end{matrix}\right)\]type means in english? Does it just mean we are going to the n-th derivative and we are on the second term or the p term or something else?

  9. anonymous
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    No its just the combinations...n items taken 2 at a time. Where order does not matter. |dw:1327353236094:dw|

  10. anonymous
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    n items taken p at a time...sorry. or 4 items taken 2 at a time as presented in the example.

  11. anonymous
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    The Binomial Theorem uses this form as well...Most notably used by Pascal and of course the Chinese .... 11 1 2 1 1 3 3 1 1 4 6 4 1 1 5 10 10 5 1 ... This represents the coefficients of the binomial powers as listed below (x+1)^1 (x+1)^2 (x+1)^3 (x+1)^4 (x+1)^5 ...

  12. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.