1.             Find an anti-derivative of f(x) = sec² (e^(3x))

                    a.     tan (e^(3x)) + c          b.    sec³(e^(3x))/9 + c

                    c.     tan (e^(3x))/3 + c      d.     csc² (e^(3x))/3 + c

    2.             Use a third degree Taylors polynomial for f(x) = sin x at x = 0 to estimate f(1).

                    a.     7/6                         b.     5/6

                    c.     .8415                    d.     .7425

    3.             If  y’ = x – xy, find y.

                    a.     y = -e ^ (1/2 x² + c) –1
 
                    b.     y = e ^ (-1/2 x²) + c

                    c.     y = -e ^ (-1/2 x² + c) + 1

                    d.     y = e ^ (1/2 x²) +c

    4.             Find the derivative of y = ln (e^(3x) + cos² x).

                    a.     (3e^(3x) - 2cos x sin x )/(e^(3x) + cos² x)

                    b.     (3e^(3x))/(e^(3x) + cos² x)

                    c.     1/(e^(3x) + cos² x)

                    d.     (3e^(3x) - 2 cos x sin x)/(e^(3x) + cos²x)

5.                 Find the speed at t = 2 when x is defined by x(t) = 3t + 4 and y is defined by y(t) = 3t²-10.
 
                        a.    3.865

                   b.    6

                   c.    4
 
                   d.    4.25
 
 
 
 
 

Grade yourself

1.    c
2.    c
3.    a
4.    a
5.   c