Questions asked by WLHE

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• Given that u=x+yi. If z=(1-i)/(u+6) is a pure imaginary number,show that y=x+6. State the values of y if x=1.?
  
• If z=a+bi and z* is the conjugate of z. Find the value of a and b when 2/z + 1/z* = 1-i. ?
  
• If #1+3^(1/2) i# is the root of the equation #2z^3+az^2+bz+4=0#,find the values of the real numbers of a and b. For the values of a and b, solve the equation. ?
  
• Show that the locus of the point P (cp,c/p) is the curve xy=c^2. Show also that the tangent at point P has the equation yp^2+x=2cp. The vertical line from the origin meets the tangent at point T. Find the locus T as p varies. ?
  
• The sum of the first n term of a series is #3-[1/3^(n-1)]#. How to obtain the expression for the #n#th term of the series, Un?
  
• The equation of two planes are given by: x+2y+z=4 and 2x-4y-z=2. Find the vector equation of the plane which contains the point (3,0,0) and is perpendicular to the two given planes. ?
  
• Given that y=cos2x/(1+sin2x) Show that (d^2y/dx^2)+2y (dy/dx)=0?
  
• Given that #v=(sin u)^(1/2)#, Show that #4v^3 (d^2v)/(du^2)+v^4+1=0#?
  
• The parametric equations of a curve are x=tan2θ and y=cot2θ.find the equations of the tangent and the normal to the curve at the point where θ=pi/6?
  
• A cone of height h cm and base radius r cm is made from a spherical solid of radius 10cm. Show that #r^2=20h-h^2#.?
  
• An aluminium foil with a surface area of 500cm2 was anodized. Gow many coulombs of electricity were required to increase the thickness of the layer by 1*10^-3 cm (density of aluminium oxide=4.0g cm-3)?
  
• How to show d/dx(tanx)^3=3 (tanx)^4+3(secx)^2-3?
  
• How to differentiate e^(xy)+1/y=5x+6?
  
• Show d/dx (cot x)=-(cosec x)^2.?
  
• Show #d/dx (cos^-1 2x)=-2/(1-4x^2)^(1/2).# If #y=sin (cos^-1 2x),#show that #(1-4x^2) (d^2y)/(dx^2)-4x dy/dx+4y=0.# How to do this?
  
• By using the substitution y=vx, find the particular solution of the differential equation 2xy (dy/dx)=y^2-x^2 when y=4 and x=2. Express y in terms of x.?
  
• Find the set of values of k,where k is a constant,when equation x^3-12x^2+45x-34=k has (a) one root (b) three roots?
  
• Find the coordinates of the points of intersection of the two curves. (y=x^2-1 & y=6/x^2)?
  
• X (du/dx)=-2cot (u) , y=ux Find the solution of the differential equation satisfying the condition y=0 when x=1. Write the answer in the form y=f (x)?
  
• F (x)=|x-5|+|x+5|. Write f(x) as a piecewise function.?