A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • one year ago

Find f if f''(x)=2e^t+3sin(t), f(0)=7, f(pi)=-8

  • This Question is Closed
  1. FireKat97
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    because you have been given f"(x) you need to integrate twice to get to f'(x) and then f(x)

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

    I have been doing that but have not gotten the correct response

  3. FireKat97
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    Can you post your working so far?

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

    I have quite a few different problems But I only have one more chance to get it right.

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

    Like I have worked them a lot

  6. FireKat97
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    but can you show me how you went about trying to solve the problem? So your working out so I can see where you're going wrong..

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

    I am not exactly sure how to take a photo and attach a file since I am on my computer.

  8. FireKat97
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    do you think you could type up your solution?

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

    its a kinda complicated solution thats why i am on here trying to get an answer for it so i an compare the correct answer to my answer to see where i went wrong

  10. FireKat97
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    okay so when you integrate 2e^x what do you get?

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

    2e^x anything e^x is still e^x

  12. FireKat97
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    yup thats correct

  13. FireKat97
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    sorry what do you get when you integrate 3sint

  14. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    -3cost

  15. FireKat97
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    Yup, thats correct too, so we know that the integral of f"(x) is 2e^t - 3cost + c

  16. FireKat97
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    so f'(x) = 2e^t - 3cost so now we have to integrate again

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

    I am running out of time its an online homework due at a specific time Can you tell me the answer? I only have one last attempt and 2/23 problems left that I have been struggling with for the past hour and a half

  18. FireKat97
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    you're not going to learn if i just tell you the answer..

  19. FireKat97
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    just try integrating f'(x) = 2e^t - 3cost + c in the same way and tell me what you get

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

    The tricky part with this question is that you have two constants since you have to integrate twice I understand the mechanics of how to do the problem and with you not telling me your answer I can't know if it is correct so if the answer you have is wrong then I am learning the wrong thing I have tried 4 different answers so if you tell me your answer I can check to see if that was one of the answers I got

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

    2e^t+3sint+cx+c

  22. freckles
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    he and you are both correct and saying f'(x)=2e^t-3cos(t)+c you can integrate first... or you can use your constraint to find c...wait isn't one of your constraints written incorrectly...one of them should be f'(a)=b where a and b are some numbers ...whichever one it is use the constraint then integrate note: if you integrate first make sure you don't use the same letter for the other constant you get after the next integration

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

    But what is the final answer that you get ?

  24. freckles
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    No one can know the problem is incorrectly stated

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

    What do you mean it is incorrectly stated ?

  26. freckles
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    As I was saying earlier isn't one of your constraints is suppose to be in the form f'(a)=b where and b are some numbers?

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

    yes it is supposed to be but the two questions I was stuck on do not give it in the form of f(x) and f'(x) which is why it is difficult But it can be done I know the steps but keep getting the wrong answer

  28. freckles
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    where a and b are some numbers*

  29. FireKat97
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    No, not necessarily.

  30. freckles
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    err... do you not have a condition on f'?

  31. FireKat97
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    In this case, because f(0) is given, cx can be eliminated giving the constant d

  32. freckles
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    you have f(0)=7 and f(pi)=-8 one of these is really suppose to be about f'

  33. FireKat97
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    what I mean is f(x) = 2e^t - 3sint + cx + d we can find d and hence when we sub in f(pi) = -8, the value of d is already known so we can find c as well

  34. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    no you are supposed to integrate twice fine the constant of the first integrated equation integrate again and then solve for the second constant and plug everything back into the integrated problem that gave the equation for f(x)

  35. FireKat97
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    because since f(0) = 7 is known, everything except d is equal to 0, so d = 7

  36. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    FireKat97 that is what I have been doing and keep getting the wrong answer Can you tell me your answer so that I can see if it is correct and then send me a picture of your work ?

  37. FireKat97
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    then we know that f(pi) = -8 = 2e^π - 3sinπ + cπ + 7 and c can now be found too

  38. FireKat97
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    I got f(x) = 2e^t - 3sin(t) + t(-15 - 2e^t)/π + 7 hoping I didn't make any silly mistakes along the way...

  39. freckles
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    I guess you guys were right about f(0)=7 and f(pi)=-8 I was just thinking they normally give a condition for each integration step but I got a different d and c above using the conditions

  40. FireKat97
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    Unless f(0) is given, something about f'(x) is required

  41. freckles
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    right I see that now

  42. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    the answer you gave was incorrect FireKat97

  43. FireKat97
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    do they need it in decimals if its an online quiz thing

  44. freckles
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    but yeah f(0)=7 doesn't give d=7 you should get 2-3(0)+c(0)+d=7 which this will give us a different c in the end also

  45. FireKat97
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    OH wait whoops! yeah

  46. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    no, no decimals

  47. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    so wait what should the answer be ?

  48. FireKat97
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    because e^0 = 1 not 0

  49. FireKat97
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    d = 5 my badddd

  50. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    so instead of 7 it should be 5 ?

  51. FireKat97
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    yeah and so when you sub d in again for f(pi) = -8, use d as 5, so c should be different too

  52. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    okay i give up I just won't get points for this problem lol

  53. FireKat97
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    don't give up, you're almost there :p

  54. zepdrix
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    broski, ask for help on a question sooner than 30 minutes before the due date! XD that's crazy sauce!

  55. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    I still don't have an answer lol so I do not feel almost there

  56. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    I have more than 30 minutes..

  57. zepdrix
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    For future reference, when you get into a jam like this, https://www.wolframalpha.com/input/?i=f%27%27%28t%29%3D2e%5Et%2B3sin%28t%29%2C+f%280%29%3D7%2C+f%28pi%29%3D-8 Wolfram is really helpful with problems such as this one. Unless your teacher considers that cheating of course :p I find it to be a useful tool to check work though.

  58. zepdrix
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yay \c:/

  59. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    I have already tried wolfram and it does not work either not for this problem

  60. FireKat97
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    i copied and pasted and forgot to get fix the 5 :p haha

  61. zepdrix
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    inputting into wolfram is a little tricky :O I think I did it correctly though, didn't i?

  62. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    so that is not the correct answer FIREKAT?

  63. freckles
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    @Asiah321 we said d=5 and you had f(t)= 2e^t - 3sint + cx + 5 so now use this other condition f(pi) = -8 plug in pi for t and replace f(pi) wth -8 and solve for c

  64. freckles
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    oops that x should be t but whatever

  65. freckles
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    solve for c: -8=2e^pi-3sin(pi)+c(pi)+5

  66. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Where is the typo ?

  67. Jhannybean
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \[f''(x)=2e^t+3\sin(t)\]\[f'(x)=\int (2e^t+3\sin(t))dt = 2e^t-3\cos(t)+c\]\[f(x) = \int (2e^t-3\cos(t)+C)dt = 2e^t-3\sin(t) +Cx+D\]\[7=2e^{0}-3\sin(0)+C(0)+D \implies D = 5\]\[-8 = 2e^{\pi} -3\sin(\pi)+\pi C+5\]\[\pi C = -2e^{\pi}-13 \qquad \implies C=\frac{-2e^{\pi}-13}{\pi}\]\[f(x) = ....\]

  68. Jhannybean
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Therefore, what im getting for \(f(x)\) is.. \[f(x) = 2e^{t}-3\sin(t)+\left(\frac{-2e^{\pi}-13}{\pi}\right)t+5\]

  69. Jhannybean
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    some variable errors. But you can figure out that much

  70. freckles
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    lol is it f(x) or f(t)

  71. Jhannybean
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Haha, it's f(t).

  72. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Jhannybean it was correct !!!! thank you so muchhhhh !!!!

  73. Jhannybean
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Whatever, it's f(o)

  74. freckles
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    I only wanted to point that out because there has been a bunch of mixing of variables in this post

  75. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    jhannybean can you check your messages please

  76. Jhannybean
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Yeah, that's why i just went with what I thought it was.

  77. Jhannybean
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    You shouldn't be thanking me, honestly. I was working it out while @freckles and @FireKat97 we're helping you solve it:P Sometimes you have to work with people instead of asking fr the answer.

  78. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    I really appreciate you all ! I have been struggling with this problem and another one for a while

  79. Jhannybean
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    post your new question in a new thread :)

  80. 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.