A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • 5 years ago

(a)find y as a function of x, if y'=e^(x-1) and y =1 when x=1. What is the y intercept of this curve? (b)The gradient of a curve is given by y'=e^(2-x) and the curve passes through the point (0,1). What is the equation of this curve? What is its horizontal axis? (c)f=Find y, given that y'=2^(-x), and y=1/2log2 when x =0. (d) It is known that f'(x) = e^x + 1/e and that f(-1)=-1. Find f(0)

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

    \[\int\limits e ^{x-1}\]

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

    \[1/e \int\limits e^x d x\]

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

    a) \[y = \int\limits_{}^{} e ^{x-1}dx\] u = x-1 du = dx \[y=\int\limits_{}^{}e ^{u}du = e ^{u}+C=e ^{x-1}+C\] 1=e^0 +C = 1+C C=0 y = e^x-1

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

    \[1/e[e^x +c]\]

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

    i actually did (a) i need help with the other ones more lol

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

    b) y = -e^2-x + C 1=-e^2 +C C = 1+e^2 \[y = -e ^{2-x} +e ^{2}+1\] c) y=-2^(-x)/ln2 +C 1/2ln2 = -1/ln2 +C C = 3/2ln2 \[y = -\frac{1}{\ln 2}(2^{-x} -\frac{3}{2})\] d) f(x) = e^x + x/e +C -1 = e^-1 -1/e +C C = -1 f(x) =e^x +x/e -1 f(0) = 1-1 = 0

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

    for c is it the same as writing y=1-2^(-x)/log2

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

    yeah well i get 3/2 or 1.5 instead of 1 but yes you could write it either way

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

    thats the answer at the back of the book lol

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

    ahh well book must be wrong..:) is it 1/2*ln2 or 1/(2ln2) for initial conditions

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

    isnt it the same thing

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

    no one the log is on top the other its on the bottom

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

    oh its 1/(2log2)

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

    thats what i thought i dont know what i did wrong on that one...

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

    when i did it i got -c=-1/2log2 -1/2log2 c=1/2log2+1/2log2

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

    theres should be no negative infront of y=-2^(-x)/ln2 +C i think lol

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

    wait is x=0 or x=1 ? no there needs to be a neg because derivative of -x = -1

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

    x = 1

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

    oh sorry i wrote it wrong

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

    thats it then lol it says 0 above

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

    yeah im sorry lol i must of did it by accident lol

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

    it happens, keeps me on my toes :)

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

    lol thanks heaps you made me learn something new today:)

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

    your welcome good luck on the rest

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

    for question (b) when you sub in x = -1 dont you just get -e

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

    f(x) = e^x + x/e +C when x=-1, = e^-1 + -1/e +C =1/e - 1/e +C =0 + C its not -e because e is in denominator

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

    oh i was looking at d)...is that right?

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

    no (b) lol

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

    ur answer is right but i tried doing it on my own and got -e :(

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

    ok y=−e^(2−x)+e^2+1 x=-1 =-e^(2-(-1)) +e^2 +1 =-e^3 +e^2 +1 ahh no you cant combine the e's because of the addition

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

    oh why are you using x=-1

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

    omg whats wrong with me lol im not reading any of the questions right im really sorry for troubling you for no reason

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

    haha no prob

  34. 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.