Quantcast

Got Homework?

Connect with other students for help. It's a free community.

  • across
    MIT Grad Student
    Online now
  • laura*
    Helped 1,000 students
    Online now
  • Hero
    College Math Guru
    Online now

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

Valdas Group Title

Finding a limit

  • one year ago
  • one year ago

  • This Question is Closed
  1. Valdas Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    \[\lim_{x \rightarrow 0} \frac{ \sqrt[5]{1+2x}-1 }{ \sin x }\]

    • one year ago
  2. myko Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    try l`hopital

    • one year ago
  3. Valdas Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    sorry, I forgot to mention that we haven't learnt about l`hopital

    • one year ago
  4. myko Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    nvm

    • one year ago
  5. myko Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    you learned Taylors series?

    • one year ago
  6. Valdas Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    Nope

    • one year ago
  7. RajshikharGupta Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    expand the root term by binomial theorem

    • one year ago
  8. RajshikharGupta Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    then there will be term like 10x/sinx and x/sinx=1 for given condition so ans =10

    • one year ago
  9. RajshikharGupta Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    while opening with binomial neglect higher degree terms

    • one year ago
  10. Valdas Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    well, the answer should be 0.4 . And what do you mean by expanding the root term by binomial theorem? Do you mean, that I should raise the fraction by the 5th degree and then use the binomial theorem and numerator?

    • one year ago
  11. RajshikharGupta Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    no see it i have shown|dw:1353844296253:dw|

    • one year ago
  12. RajshikharGupta Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    and i have done mistake while doing this it is 2/5=0.4 so sorry for that

    • one year ago
  13. Valdas Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    Could you explain how did you get \[\sqrt[5]{1+2n}=1+\frac{ 2 }{ 5 }n + ....?\]

    • one year ago
  14. RajshikharGupta Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    it is binomial theorem u will learn this in algebra in high school it is (1+x)^n=1+(nC1)x+(nC2)x^2+(nC3)x^3 and so on .....

    • one year ago
  15. Valdas Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    Yes, I know the binomial theorem, but how does it apply to roots? I thought that the power of polynomial it is raised to must be an integer to apply this theorem.

    • one year ago
  16. RajshikharGupta Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    no it can be applied on roots if x is very small and it can even for any fractional powers for same case it quite valid approximation tool in maths and physics u can conform it with ur teachers

    • one year ago
  17. Valdas Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    Perhaps anyone can think of other way to find the limit? Every problem until this one required some sort of quite simple algebraic manipulation.

    • one year ago
  18. RajshikharGupta Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    actually it is one of the shortest methods but indeed u can initiate in ur problem by factorizing the numerator term

    • one year ago
  19. pasta Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    Binomial theorem just makes work hard ,learn l hopitals rule it is easy.LOOK IF after substituting the limit you get 0/0 differentiate the numenartor and denominator independently the find the limit three steps

    • one year ago
  20. Valdas Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    I can't use l'hoptial's rule to find the limit

    • one year ago
  21. pasta Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    i do not get you.Do you mean ,you are not allowed to use l hopitals rule or you can not evaluate.

    • one year ago
  22. Valdas Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    We haven't studied about that rule yet

    • one year ago
  23. pasta Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    do u want to learn it?

    • one year ago
  24. Valdas Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    This problem can be solved without use of l'hopitals rule, I want to find out how. Perhaps there is some simple algebraic trick which could be used to find the limit or something like that

    • one year ago
  25. shubhamsrg Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    @RajshikharGupta 's method seems to be the shortest to me,

    • one year ago
  26. pasta Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    ok ,I SEE.I have two solutions so far ,binomial and l'hopitals.But looks like there are one's and may be try following the trigonometry side or otherwise am still checking

    • one year ago
  27. shubhamsrg Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    are you asking how do we get (1+x)^n = 1+xn (given |x|<1 ) ?

    • one year ago
  28. Valdas Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    Yeah, I don't underst that part

    • one year ago
  29. shubhamsrg Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    hmm,,heard of taylor series expansion ?

    • one year ago
  30. Valdas Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    No

    • one year ago
  31. shubhamsrg Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    then you might just wanna mug up this formulla : |dw:1353848320044:dw| you'll get to know how we get this when you learn taylor series..

    • one year ago
  32. shubhamsrg Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    make that substitution in your question.. you'll reach the ans directly then..

    • one year ago
    • Attachments:

See more questions >>>

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.