Math 125  Test 2    4 points each Feb 19, 2004

 

 


Differentiate, (means find yÕ(x).

 

1.  y = 4

 

2.  y  = x

 

3.  y = 4x2 - 5

 

4.  y = sin 3x

 

5.  y = csc (x/4)

 

6.  y = tan Ãx

 

7. 

 

8. 

 

9.  y = x2 sin x

 

10.  y = x + cot x

 

11. 

 

12. 

 

13. 

 

14.  y = sin2 (x2)

 

15.  y = cos 3x sin 2x

 

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16.  Find y Ô = dy/dx

 

x3 y2 - y = x

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17.  Find the equation of the tangent line to

 x cos y = 1 at the point (2, ¹/3).

 

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18.   Find  for x2 - y2 = 16

 

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19.  Find f(4) if

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20.  Find the point(s) at which  has a horizontal tangent line.

 

 

 

Bonus: 10 points

 

1.  If you are given that if f(x) = ex, then f ' (x) = ex, what can you conclude about the limit

  ?