BC Calculus Review Assignment                            Name ___________________________


Problem 1.  

Find dy/dx for each of the following. Make sure to show all your work in a clear and concise manner.

A.   y = sqrt(x^3+1)                                                                                     Simplified Answer:





B.   y = (x^2+x-1)/(x^2-1)                                                                                  Simplified Answer:





C.   y = -x*tan*x                                                                                      Simplified Answer:




D.   y = (x+1)^x                                                                                   Simplified Answer:




Problem 2.  

Find the following antiderivatives. Make sure to show all your work in a clear and concise manner.

A. 2/3*Int(x^(-1/3),x)                                                                                  Simplified Answer:





B. Int(cos(x)/sqrt(sin(x)),x)                                                                                     Simplified Answer:






C. Int(sqrt(cot(x))*csc(x)^2,x)                                                                         Simplified Answer:





D. Int(x*sqrt(2*x+1),x)                                                                                     Simplified Answer:






Problem 3.  

Use implicit differentiation and the equation x^2+3*xy+y^3 = 10 to find   dy/dx  .  Make sure to clearly show all your work.


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Problem 4.  

A particle P is moving along the graph of   y = sqrt(x^2-4),   2 <= x, such that the x-coordinate is increasing at the rate of 5 units per second, i.e. `x'`(t) = 5. How fast is the y-coordinate of P increasing when x = 3 ?






Problem 5.  

Find the dimensions of the rectangle of maximum area,with sides parallel to the coordinate axes, that can be inscribed in the ellipse given by   x^2/144+y^2/16 = 1 .