1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Math question

  1. Dec 24, 2004 #1
    I'm not quite sure what the question is asking:
    "If [tex]f(x)=e^xsin(x)[/tex], then the number of zeros of [tex]f[/tex] on the interval [o,2pi] is?"

    I took the derivative of this and found where it was equal to zero:
    [tex]f(x)=e^xsin(x)[/tex]
    [tex]f'(x)=e^xsin(x)+e^xcos(x)[/tex]
    [tex]0=sin(x)+cos(x)[/tex]

    I got zero. However, tha answer is 3, any suggestions?
     
  2. jcsd
  3. Dec 24, 2004 #2
    No, it wants where the function is zero, not where the gradient of the curve is zero. Where is sin x zero in that interval?
     
  4. Dec 24, 2004 #3
    you mean when [tex]0=e^xsin(x)[/tex]?
     
  5. Dec 24, 2004 #4

    dextercioby

    User Avatar
    Science Advisor
    Homework Helper

    [tex] e^{x}\sin x=0\Rightarrow \sin x=0 [/tex]
    Solve the last equation on the interval [itex] [0,2\pi] [/itex]

    Daniel.
     
  6. Dec 24, 2004 #5

    Yes, yes I do (sorry had to lengthen my post).
     
  7. Dec 24, 2004 #6
    it's is zero when x=0, x=pi, x=2pi

    so it hits three times!

    thanks! Also, why doesnt the e^x make a difference?
     
  8. Dec 24, 2004 #7

    dextercioby

    User Avatar
    Science Advisor
    Homework Helper

    It never annulates.Not even for complex arguments.

    Daniel.

    EDIT:Cause it never annulates,it does not affect the zero-s of the function.Plot the graph of 'f'.U'll see quite an interesting behavior.It has no limit for x->+infty.At minus infty it goes to zero.
     
    Last edited: Dec 24, 2004
  9. Dec 24, 2004 #8
    so e^x only increases the sinX amplitude, never now far it streatchs, so it doesnt effect how many times sinX crosses the x-axis
     
  10. Dec 25, 2004 #9

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    "Annulates"??? I assume you mean "is never equal to 0" but the only definition I can find of "annulate" is "ring shaped".

    UrbanXrises: It's not so much that it is 'always increasing'. In order to solve AB= 0, you solve A= 0 and B= 0. Since ex is never 0, The only solutions of exsin(x)= 0 are where sin(x)= 0.
     
    Last edited: Dec 25, 2004
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Math question
  1. Math question (Replies: 7)

  2. Maths Question (Replies: 3)

  3. Math question (Replies: 2)

  4. Math question (Replies: 2)

  5. Math questions (Replies: 1)

Loading...