Calculus 1  Hour Exam 3  (continued) -   Math 220     Fall, 2011

 

 

 

9.

 

Suppose that a polynomial  f  satisfies the following conditions.

 

         f(1) = 8,    f’(1) = 2     f ‘’(1) = 3   f ‘’’ (1) = 5

 

Use a linear approximation to estimate the value of  f(0.8).  Simplify and write your

answer in decimal form.

 

Answer:  7.6

 

 

 

 

 

 

 

 

 

 

 

 

10.

 

 

 

 

 

 

 

Suppose that  F  and  F’  are each differentiable (and thus continuous) everywhere and

That  r  and  s  are constants.  Select the choice below which most clearly states part

2 of the Fundamental Theorem of Calculus.

 

             s                                                   s

a.        ∫ F’(t) dt  =  F’(r) – F’(s)          b. ∫ F(t) dt  =  F’(r) – F’(s)          

r                                                    r

 

           s                                                 s

      c.  ∫ F’(t) dt  =  F(r) – F(s)          d. ∫ F(t) dt  =  F(r) – F(s)          

          r                                                  r

 

           s                                                    s

      e.  ∫ F’(t) dt  =  F’(s) – F’(r)          f.  ∫ F(t) dt  =  F’(s) – F’(r)          

          r                                                     r

 

           s                                                  s

      g.  ∫ F’(t) dt  =  F(s) – F(r)          h.  ∫ F(t) dt  =  F(s) – F(r)          

           r                                                  r

 

 

Answer:  g