Calculus 1  Hour Exam 1 (continued)   -   Math 220     Spring, 2010

 

 

5.

 

 

Given that  f(x)  =  5  +  ln(x – 4),  find a formula for  f -1 (x).

 

Answer:  f -1 (x)  =  4  +  e x – 5

 

 

 

6.

 

Let   f(x)  =  x2  -  6x.   Use the definitioin of a derivative as a limit to show that

f ‘(x)  =  2x  -  6.  Show each step in your calculation and be sure to use proper terminology.

 

 

 

7.

 

 

Find the domain of the function    f(x)  =  ln ( 5 -  √ ( x – 30) .

 

Answer:  [ 30, 55 )

 

 

 

 

8.

 

 

Find a formula for an exponential function whose graph goes through the following

three points.     (0,9),   (3,12),   (6,16)

 

Answer:  y(x)  =  9 (4/3)x/3

 

 

 

 

 

 

 

 

 

 

 

9.

 

 

Evaluate the following limits.  An answer of  “does not exist” is not sufficient.  If the

limit is infinite, then you must state if it is  ∞   or   -∞ .

 

a.                                lim  ( 18  -  11 ln (5x2  +  1 ) )

                       x → 0

 

b.                              lim  ( 9  +  8 cos (e -3x ) )

                       x → ∞

 

 

c.                               lim  ( x2  +  2x  -  25) / ( x – 5 )

                       x → 5

 

d.                              lim  ( 3x2  +  10 ) / ( x2  -  16 )

                       x → 4 -

 

e.                                lim  ( 3x  +  5x2 ) / ( 7x2  +  13 )

                       x → ∞

 

 

answers:  a.  18        b.  17       c.  12     d.  - ∞     e.  5/7

 

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