Quantcast

A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

DLS

  • 2 years ago

Limits

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

    @mathslover

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

    It is easy , it just looks long. I will do that after lunch, ok?

  3. DLS
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \[\Huge \lim_{x \rightarrow 0}( \frac{1}{x} \int\limits_{0}^{a} e^{\sin^{2}t}dt-\int\limits_{x+y}^{a} e^{\sin^{2}t}dt)\]

  4. DLS
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Okay @mathslover and I know it is easy,I was trying it but i think the first term will cancel off because a and y both are constants maybe..i can be wrong,just drop a hint.

  5. DLS
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    sorry the term 1/x is outside everything

  6. yrelhan4
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    we can write the expression as.... (first term) + ∫ e^(sin^2 t dt) with limits ... a to x+y.. the sign changed on reversing the limits..

  7. yrelhan4
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    now combining the two limits.. 0 to a and a to x+y .. 0 to x+y ..

  8. yrelhan4
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    because the integrand is same..

  9. DLS
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    0 to a and 0 to x+y=0 to x+y

  10. yrelhan4
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    yep.

  11. DLS
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    cool :O

  12. DLS
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \[\Huge \frac{1}{x} e^{\sin^{2}x+y}\]

  13. DLS
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    differenatiate and bingo :O

  14. DLS
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    e^sin^2x+y

  15. yrelhan4
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    why did you not do anything to 1/x ?

  16. yrelhan4
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    multiplication theorem.. hmm..

  17. DLS
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    1/x was outside the integral sorry :P

  18. yrelhan4
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    aur jab 0 put krenge.. to bhi to kuch aayega. vo kahan gyi? :P

  19. DLS
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Wait.Lets start again :|

  20. DLS
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \[\Huge \lim_{x \rightarrow 0} \frac{1}{x}(\int\limits_{y}^{a}e^{\sin^{2}t} dt-\int\limits_{x+y}^{a}e^{\sin^{2}t} dt)\]

  21. DLS
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    original question^

  22. DLS
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \[\Large \lim_{x \rightarrow 0} \frac{1}{x}(\int\limits_{y}^{x+y}e^{\sin^{2}t} dt)\] On changing the sign and revevrsing the limits and combining them

  23. yrelhan4
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    acha vo 'a' vala to 0 ho jayega.. a ki differentiation 0.. but hamne x+y ko differentiate bhi nhi kra.. :/

  24. DLS
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Apply LH Rule

  25. yrelhan4
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    @shubhamsrg ?? :)

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

    kya hua? kya dikkat hai ? (:

  27. DLS
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \[\Huge e^{\sin^{2}{x+y}}(1+\frac{dy}{dx})-e^{\sin^{2}y} \frac{dy}{dx}\]

  28. DLS
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    put dy/dx=0

  29. yrelhan4
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    why put dy/dx=0 ?

  30. DLS
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \[\Huge e^{\sin^{2}x+y}\] answer

  31. DLS
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    y is behaving as a constant,we assume y independent of x

  32. DLS
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    idk what i wrote please someone explain :P

  33. yrelhan4
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    ohhh.. achaaaa..

  34. DLS
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    If we are driving a car and chasing a thief on a bike then the rate of change of our speed won't affect the speed of the theif's bike

  35. yrelhan4
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    limit y se x+y ?? how??

  36. DLS
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    tune he to bataya?:/

  37. yrelhan4
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    i said 0 to x+y.. :/

  38. DLS
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    y->x+y hoga

  39. DLS
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    wo "A" hai 0 nahi :|

  40. yrelhan4
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    ohh. ok.

  41. DLS
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    :)

  42. DLS
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    but still didnt get it :|

  43. DLS
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \[\LARGE e^{\sin^{2}x+y}\] differentiating this^

  44. DLS
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \[\LARGE e^{\sin^{2}x+y} \times \sin2x(+0)\]

  45. DLS
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \[\LARGE e^{\sin^{2}y}\] Differentiating the lower limit^

  46. DLS
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \[\LARGE e^{\sin^{2}y}=>e^{\sin^{2}y} \times \sin2y\]

  47. DLS
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    lower limit will become 0

  48. DLS
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    I'm left with.. \[\LARGE \frac{1}{x}e^{\sin^{2}x+y} \times \sin2x\]

  49. yrelhan4
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    abbe yr. x ki differentiation 1 hogi.. LH me numerator aur denominator alag alag diff krte hain.. :/

  50. DLS
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    maine bhi to wahi bola tha BC

  51. DLS
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    BUT 1 KA 0

  52. yrelhan4
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    to x ki diff 1 ho jayegi.. aur numerator me tune jo kra tha. dy/dx=0 krke aa jayega ans.

  53. yrelhan4
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    kya 1 ka 0? 1 baari diff krenge.. :/

  54. DLS
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    1/x hai to 1 ka karenge to 0 x ka karenge to 1 0/1=0

  55. yrelhan4
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    lol. 1*x ki diff. 0*x + 1*1.. lol

  56. yrelhan4
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    to upar sirf 1 thodi hai.. baaki bhi to hai. usse multiply krega saara.. to 1* ....... = ......... aa jayega.. :O

  57. DLS
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    badiya hai :|

  58. DLS
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    par sin2x kahan gaya?

  59. DLS
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    main question :P

  60. yrelhan4
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    newton lebinitz me integrand ki differentiation nhi krte.. limits ko integrand me daalte hain multiply by limits ki diff..

  61. DLS
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    medal medal medal medal medal medal medal medal medal medal medal medal medal medal medal medal medal medal medal medal medal medal medal medal medal medal medal medal :*

  62. yrelhan4
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    :')

  63. DLS
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    seekho @shubhamsrg

  64. yrelhan4
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    lol. meri bezti badi achi krte ho aap log. :/

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

    maine upar kuch padha bhi nahi kya likha hai :3

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

    What's the answer then? xD

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

    @yrelhan4 is the answer to all the questions . O:)

  68. yrelhan4
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    :')

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

    Great xD I thought in a way to solve it but if it's already solved then ok (:

  70. 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.