Answers edited by Frederico Guizini S.

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• Question #5698e
  
• How do you find the area of the common interior of #r=4sintheta, r=2#?
  
• How do you integrate #ln (x^2+14x+24)dx#?
  
• How do you evaluate #int (x^3 + 2x^2 + 5x - 2)/(x^2 + 2x + 2)^2 dx#?
  
• How do you integrate #(6x^2-x-1)/(3x-1)# using partial fractions?
  
• How do you find the critical points for #f(x) = 2x^(2/3) - 5x^(4/3)# and the local max and min?
  
• What is the equation of the line tangent to # f(x)=(e^x-sinx)/(x-xcosx) # at # x=pi/3#?
  
• The region under the curves #x=0, x=y-y^4# is rotated about a) the x axis and b) the y axis. How do you sketch the region and find the volumes of the two solids of revolution?
  
• How do you differentiate #y=r/sqrt(r^2+1)#?
  
• How do you integrate #int xroot3(4+x^2)# from [0,2]?
  
• How do you integrate #[6/(x-3)^4*(x^2-4x+4)]# using partial fractions?
  
• How do you differentiate #f(x)= e^x/(xe^(x) -x )# using the quotient rule?
  
• How do you use the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region #y= sqrt x#, #y=0# and #y=(x-3)/2# rotated about the x-axis?
  
• What's the derivative of #arctan [(1-x)/(1+x)]^(1/2)#?
  
• How do you find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line: y= x, #y = sqrt(x)#; about x = 2?
  
• How do you determine where the function is increasing or decreasing, and determine where relative maxima and minima occur for #f(x) = 3x^4 + 16x^3 + 24x^2 + 32#?
  
• Question #25ffa
  
• What is the derivative of #f(t) = ((lnt)^2-t, sec(1-t) ) #?
  
• How do you integrate? dx/sqrt(4x^2-8x-1)
  
• How do you find the antiderivative of #int sqrt(9+4x^2) dx#?
  
• How do you integrate #int sec^2x/(1+tanx)^3# using substitution?
  
• I really don't understand this calculus 2 problem?
  
• What is #int1/(x^2-5)#?
  
• How do you find critical point for this equation #f(x,y)=6x^7+7y^2+8xy+9#?