Work to Work on
1)
Use the limit definition of a derivative (this was mentioned in class) to derive:
y
=
1
࠵
This problem has actually been fully done in class. On a test this would be a little more difficult
of a problem, because there are a few steps. Just remember to simplify what is inside the limit,
combine like terms, and then evaluate. To get credit you must solve it using the limit definition.
2)
List out the four rules that have been mentioned in class and listed out. Identify which step they
have been used in:
࠵
=
3
࠵
!
+
5
࠵
!
+
10
࠵±
࠵±
=
࠵
࠵±
(
3
࠵
!
+
5
࠵
!
+
10
)
࠵
!
=
!
!"
3
࠵
!
+
!
!"
5
࠵
!
+
!
!"
(
10
)
__________________(a)
࠵
!
=
!
!"
3
࠵
!
+
!
!"
5
࠵
!
+
0
__________________(b)
࠵
!
=
3
!
!"
࠵
!
+
5
!
!"
(
࠵
!
)
__________________(c)
࠵
!
=
3
2
࠵
+
5
(
3
࠵
!
)
__________________(d)
3)
Assume you are driving your car on the freeway and you look down at the speedometer and
read 60 mph (which is the same as 1 mile/minute). How far would you have expected to have
travelled after driving
another 30 seconds
__________________(a)
another minute
__________________(b)
another 5 minutes
__________________(c)
another hour
__________________(d)
another 5 seconds
__________________ (e)
(please leave in fractional form if appropriate)
Which estimate would you expect to be most accurate and why?
(hint: read over section 3.6 and remember that the speedometer would be the
velocity
of the
car)