Quantcast

A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

Bonrozzy

  • one year ago

Find the value of k that the line x=k divides the area of the first quadrant region of y=e^-x and the x-axis x >= 1 into two equal parts.

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

    So you have talked about improper integrals?

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

    yes

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

    so we want this: \[1/2 \int\limits_{1}^{k}e^{-x} dx=\lim_{a \rightarrow \infty}\int\limits_{1}^{a}e^{-x} dx\]

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

    we want that one area to be half of that other area

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

    did you get this far?

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

    i see

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

    I hadn't thought about constructing it that way. It makes sense.

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

    so we can try to evaluate both integrals first then we just solve the equation for k

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

    That's true haha it seems so simple now thank you :)

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

    I get that k=1, but i know that's not the answer.

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

    what is the answer? also yep if k is one, then that one area is 0 and we know 0 is not half the other area

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

    \[-1/e^k = 1/e\]

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

    sorry it wouldnt be one, but this is the end result i believe

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

    that negative is weird killing me because e^(to a positive number) can't be negative

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

    i was agreeing it isn't 1 because it would give us 0 for that one area

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

    the antiderivative of e^-x is -e^x right?

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

    -E^-x*

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

    maybe since we can't solve that equation for k there is no way possible to divide the area with a vertical line so we have two equal areas on both sides

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

    yep you are right

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

    Okay, well here's some help. plugging the e^-x in my calculator and then taking the integral of that I find the area, i divided it by 2 and then checked the x y table to find the x that gives half the area. It is about 1.693

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

    i got it

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

    i wrote the equation just a little wrong

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

    oh

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

    \[ \int\limits\limits_{1}^{k}e^{-x} dx=1/2 \lim_{a \rightarrow \infty}\int\limits\limits_{1}^{a}e^{-x} dx\]

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

    you will get the answer you got using your calculator except it will be exact

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

    i'm idiot sorry

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

    oh such an easily overseen mistake! Ill check this out right now hahhaaha it's perfectly fine :D thanks for taking the time to figure it out!

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

    Did you get it?

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

    \[-1/e^k+1/e=1/2e\]

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

    thats the function right?

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

    yep good so far

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

    Then just solve for k?

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

    yep! :) I left it as \[e^{-k}+e^{-1}=e^{-1}/2 \]

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

    oops with a negative in front of the e^(-k)

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

    \[-e^{-k}+e^{-1}=1/2e^{-1} => -e^{-k}=-1/2 e^{-1} \]

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

    get rid of those negatives then take natural log of both sides

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

    Yes I got it! Thank you so much :) it's gonna be: \[-\ln (1/2e)\]

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

    or you could write it as ln(2e)

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

    true haha

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

    but yep if you put that in your calculator you will see that its approximation is the same as the approximation you got using just the calculator to find what was it 1.6 something

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

    Yes I noticed that haha. I can't thank you enough.

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

    I'm going to need to learn that cool calculator trick for myself

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

    I'm rather inept at using the calculator, but that's one trick I know ;)

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

    i know the basics and i know there are really cool tricks in stuff i could learn just never got around to it

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

    anyways fun problem we are going over improper integrals today in class :)

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

    cool.

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

    Well, where i am it's just about dinner time. Thanks again it really saved a lot of hair pulling. See ya

  48. 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.