Download MSWord Format

Math 180 #003
UNM
Summer 2012
Elements of Calculus I: Worksheet 2 KEY
1. 1B, 2D, 3G, 4E, 5A, 6C, 7F.
2. (a) 160 ft/sec.
(b) 96 ft/sec.
(c) 10 sec.
(d) -160 ft/sec.
3. 1D, 2B, 3A, 4C.
4. (a) 100 units and 200 units.
(b) When 20 units are sold, the profit is increasing at a rate of $2.60/unit.
5. (a) x  1 : lim f ( x) DNE and f (1)  0 . Thus, lim f ( x)  f (1) .
x 1
x 1
x  4 : lim f ( x)  2 and f (4) is undefined. Thus, lim f ( x)  f (4) .
x 4
x4
(b) x  3 : Vertical tangent line. x  1 : Discontinuous. x  2 : Sharp corner. x  4 :
Discontinuous.
6. (a) Continuous everywhere. Not differentiable at x  3 .
(b) Discontinuous and not differentiable at x  2 .
(c) Continuous and differentiable everywhere.
(d) Continuous and differentiable everywhere.
7. (a) f ( x)  x 2 . f '(2) .
(b) f ( x)  1/ x . f '(10) .
8.
1, x  0
. (Note: f '( x) is undefined at x  0 .)
f '( x)  
 1, x  0
9. (a) False.
(b) True.
(c) True.
(d) False.
10. f ( x)  x is continuous at x  0 , but not differentiable at x  0 .
Page 1/1