Differentiating sin(x) from First Principles - Page 11

Questions
  • How do I use this proved result for the Dirac Delta function to evaluate the following integral involving a Dirac Delta function of a function?
  • #y(x,t) = Ce^(iomegax//c)e^(-iomegat) = Ce^(ialpha)#, where #alpha = (2pix)/lambda - 2pi nut#... Show that for standing waves, #y(x,t) = Asin((npix)/L)sin(2pin nu_0 t + delta)#? You may want to note the boundary conditions of a vibrating guitar string.
  • What is the derivative of cos^4(x) + cos (x^4)?
  • How to solve ∫ tanx dx ?
  • If integral DX / x(x4+1) DX is equal to ?
  • Find the following #int 4 (1/x-e^-x)cos(e^-x +lnx)dx#?