Math 1910, Calculus I

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Instructions.  Choose the response which best answers the question. A score of 7 out of 10 is required for successful completion of MATH 1910.

1. Which of the following is the value of the limit
   

   lim x® 2    x2-2x x2-6x+8

   (a)

   -2

   (b)

   -1

   (c)

   0

   (d)

   1

   (e)

   does not exist

2. Which of the following is the value of the limit
   

   lim x® 1    x4-1 x2-2x+1

   (a)

   -2

   (b)

   -1

   (c)

   0

   (d)

   1

   (e)

   does not exist

3. Which of the following is the value of the limit
   

   lim x® ¥    x2-2x x2-6x+8

   (a)

   -2

   (b)

   -1

   (c)

   0

   (d)

   1

   (e)

   does not exist

4. Which of the following is the derivative of f( x) = x²+3x+2?

   (a)

   2x+5

   (b)

   2x

   (c)

   3

   (d)

   2x+3

   (e)

   0

5. Which of the following is the derivative of

   

   (a)              (b)       (c)      (d)      (e)  0

6. Which of the following is the derivative of f( x) = sec( x) sin( 2x) ?

   (a)	2sec( x) tan( x) cos( 2x)		(d)	sec( x) sin( 2x) +sec( x)tan( x) cos( 2x)
   (b)	-2sec( x) tan( x) cos( 2x)		(e)	sec( x) tan( x) sin( 2x)+2sec( x) cos( 2x)
   (c)	sec( x) [ sin( 2x) +2cos(2x) ]

7. Which of the following is the derivative of f( x) = tan( x³) ?  

   (a)

   sec( x3)

   (b)

   sec2( x3)

   (c)

   sec( 3x2)

   (d)

   sec2(3x2)

   (e)

   sec2( x3)  3x2

8. Which of the following is the derivative of
   

   f( x) = sin( x) 2-cos( x)

   (a)  2cosx-1 ( 2-cosx) 2     (b) cos( x) ( 2-cosx) 2     (c)  1 ( 2-cosx) 2     (d) cos( x) 2+sin( x)         (e)  cos( 2x) ( 2-cosx) 2

9. Which of the following is the derivative of f( x) = sin²( x³+1) ?

   (a)	2cos( 3x2)		(d)	2cos( x3+1)3x2
   (b)	2sin( x3+1)   3x2		(e)	2sin(x3+1) cos( 3x2)
   (c)	2sin( x3+1) cos( x3+1)   3x2

10. If y² = x²y+1 implicitly defines y as a function of x, then what is y' ?
    

    (a) 2xy    (b)  2xy 2y-x2   (c)  1 2y-x2   (d)  2x y2   (e)  2x y