Answers edited by Ken Rubenstein

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• What is the equation of the line that is normal to #f(x)=e^xcos^2x -xsinx # at # x=-pi/3#?
  
• How do you find the volume of the solid formed by rotating the region enclosed by ?
  
• What is the volume of the solid produced by revolving #f(x)=x^3-2x+3, x in [0,1] #around the x-axis?
  
• What is the equation of the line that is normal to #f(x)= x/sqrt( 3x+2) # at # x=4 #?
  
• What is the volume of the solid produced by revolving #f(x)=e^xsinpix, x in [0,2] #around the x-axis?
  
• How do you use the ratio test to test the convergence of the series #∑ 11^n/((n+1)(7^(2n+1)))# from n=1 to infinity?
  
• What is the surface area of the solid created by revolving #f(x) =e^(4x)-e^(2x) , x in [1,2]# around the x axis?
  
• How do you integrate #int 1/sqrt(-e^(2x) +9)dx# using trigonometric substitution?
  
• How do you integrate #int (4^(7x)) / (5^(2x)) # using integration by parts?
  
• What is the equation of the line that is normal to #f(x)=(x+4)^2/e^x# at # x=-1 #?
  
• How do you determine if the improper integral converges or diverges #int (x^3 + x)/((x^4 + 2x^2 + 2)^(1/2))dx# from 1 to infinity?
  
• How do you solve #x+y-z=-2#, #2x-y+z=5#, and #-x+2y+2z=1# using matrices?
  
• How do I rotate the axes of and then graph #7x^2 - 6sqrt3xy + 13y^2 - 16 = 0#?>
  
• How do you integrate #int 1/sqrt(e^(2x)+12e^x-45)dx# using trigonometric substitution?
  
• What are the points of inflection of #f(x)= x/e^(x^2) - x^2e^x #?