Results 1 to 2 of 2

Math Help - number of solution

  1. #1
    Member
    Joined
    Nov 2010
    Posts
    112

    number of solution

    the number of solution of 2^(cos x)=abs(sin x) in (0,pi) is
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Behold, the power of SARDINES!
    TheEmptySet's Avatar
    Joined
    Feb 2008
    From
    Yuma, AZ, USA
    Posts
    3,764
    Thanks
    78
    Quote Originally Posted by ayushdadhwal View Post
    the number of solution of 2^(cos x)=abs(sin x) in (0,pi) is
    If you take the log of both sides of the equation you get

    \ln(2)\cos(x)=\ln(|sin(x)|)

    The sine function from zero to Pi over 2 goes from zero to 1 and is increasing on that interval. The graph is symmetric over the line x=PI/2.

    This tells us that

    f(x)=\ln|\sin(x)|\le 0 increase from negative infinity to zero at x=Pi/2 and then decreases from 0 to negative infinite at Pi.

    the function

    g(x)=\ln(2)\cos(x) has one zero at x =Pi/2 and decreases from ln(2) to negative ln(2) on the interval.

    So this has one solution when x=Pi/2. Since both functions are monotone decreasing on Pi/2 Pi and

    \lim_{x \to \pi}g(x)=-\ln(2) \quad \lim_{x \to \pi}f(x)=-\infty

    They will cross exactly one more time in the inteval \left( \frac{\pi}{2},\pi\right)
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. number of solution of x*x =1 (mod n) ??
    Posted in the Number Theory Forum
    Replies: 7
    Last Post: May 5th 2013, 05:33 AM
  2. number of solution
    Posted in the Calculus Forum
    Replies: 0
    Last Post: January 3rd 2011, 01:56 AM
  3. number/solution problem
    Posted in the Algebra Forum
    Replies: 4
    Last Post: August 18th 2008, 10:25 AM
  4. Complex number solution for theta
    Posted in the Pre-Calculus Forum
    Replies: 4
    Last Post: June 6th 2008, 09:45 AM
  5. [SOLVED] Complex number solution
    Posted in the Advanced Math Topics Forum
    Replies: 2
    Last Post: January 23rd 2008, 10:39 AM

Search Tags


/mathhelpforum @mathhelpforum