Math 113 Hw 5 Worksheet With Answers (Page 3 of 5) in pdf

Math 113 Hw 5 Worksheet With Answers Page 3

6. Exercise 2.7.12. Shown are graphs of the position functions of two runners, A and B, who

run a 100-m race and ﬁnish in a tie.

(a) Describe and compare how the runners run the race

Answer: A runs the race at a constant speed, never speeding up or slowing down. B

accelerates throughout the race, starting out slower than A and, by the end, running

faster than A.

(b) At what time is the distance between the runners the greatest?

Answer: Based on the graph, it appears that they are furthest apart after 8 seconds,

when they are approximately 30 meters apart.

Answer: The two graphs appear to have the same slope (i.e., velocity) 9 or 10 seconds

into the race.

7. Exercise 2.7.20. Sketch the graph of a function g for which g(0) = g (0) = 0, g ( 1) =

g (1) = 3, g (2) = 1.

Answer:

8. Exercise 2.7.22. If g(x) = 1

, ﬁnd g (0) and use it to ﬁnd an equation of the tangent line

to the curve y = 1

at the point (0, 1).

Answer: Since g(0) = 1, the slope of the tangent line to the curve y = 1

is given by

g (0). Now, by deﬁnition,

(0 + h)

g(0 + h)

g(0)

g (0) = lim

= lim

Now, so long as h = 0, we have that

. Therefore,

lim

= lim

= 0

since h

0 as h

Thus, the tangent line is horizontal; the only horizontal line through (0, 1) is the line y = 1,

so we see that the equation of the tangent line is y = 1.

Math 113 Hw 5 Worksheet With Answers Page 3