Answers edited by Equivirial

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• Question #c8269
  
• How do you prove #cos^-1 x + tan^-1 x = pi/2#?
  
• How do you find the derivative of #tan(x+y)=x#?
  
• How do you calculate the change in momentum of an object?
  
• Question #14120
  
• How do you use definition of derivatives to solve the derivative of #f(x)=–2(sin(x)^5)#?
  
• How do you find the Maclaurin series of the function #f(x)=5cos(10x^2)#?
  
• The surface temperature of Arcturus is about half as hot as the Sun’s, but Arcturus is about 100 times more luminous than the Sun. What is its radius, compared to the Sun’s?
  
• A cylinder is inscribed in a right circular cone of height 6 and radius (at the base) equal to 5. What are the dimensions of such a cylinder which has maximum volume?
  
• An object has a mass of #3 kg#. The object's kinetic energy uniformly changes from #75 KJ# to #135 KJ# over #t in [0, 9 s]#. What is the average speed of the object?