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Math 110 Calculus 1

Please answer all the questions below.

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2. The table gives the position of a particle moving along
the x-axis as a function of time in seconds, where x is in
meters. What is the average velocity of the particle
fiomt=0tot=4? 27(t) answer : -1 4. Figure 2.6 shows a particle's distance from a point. What
is the particle’s average velocity fromt = 0 to t = 3‘?
disim (mate's) 3(a) 5
3
1
H590}
2 4
Figure 2.6 “Swer : 1 6. At time t in seconds. a particle‘s distance 3(t). in mi—
crometers (pm). from a point is given by s(t) = e‘ — 1.
What is the average velocity of the particle from t = 2 to t = 4? answer : (e4-ez)/(4-2) 8. In a time of t seconds, a particle moves a distance of .9
meters from its starting point, where s = 3t? (a) Find the average velocity between t = 1 and t =
1+am
(i) h = 01, (ii) h = 0.01, (iii) h = 0.001. (11) Use your answers to part (a) to estimate the instan-
taneous velocity of the particle at time t = 1.

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22. Find the average velocity over the interval 0 S t S 0.2,
and estimate the velocin at t = 0.2 of a car whose posi-
tion. .9. is given by the following table. t(scc) 0 0.2 0.4 0.6 0.8 1.0
5(ft) 0 0.5 1.3 3.8 6.5 9.6 Use algebra to evaluate the limits in Problems 25— 26. 2 3
25_ um W 26, um (1_+’l)__1.
h—m h h—HD h
Homework (3) l. The table shows values of fire) = :03 near a = 2 (to
three decimal places). Use it to estimate f ’ (2). a: 1.998 1.999 2.000 2.001 2.002
x3 1.976 7.988 8.000 8.012 8.0%: 3. The income that acompany receives from selling an item
is called the revenue. Production decisions are based.
in part, on how revenue changes if the quantity sold
changes; that is, on the rate of change of revenue with
respect to quantity sold. Suppose a company‘s revenue.
in dollars. is given by R{q) = 100:; — 10:12, where q is
the quantity sold in kilograms. (a) Calculate the average rate of change of R With re-
spect to q over the intervals 1 S q S 2 and
2gq5& (b) By choosing small values for h, estimate the instan-
taneous rate of change of revenue with respect to
change in quantity at q = 2 kilograms. 1]. Figure 2.19 shows the graph of 1". Match the derivatives in the table with the points a, b, c, d, e. Figure 2.19

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Figure 2.19
Use algebra to evaluate the limits in Problems 35-40.
35. lim
(-3+ h)2 -9
h-0
h
37. lim
1/(1 + h) - 1
h-+0
h
Find the derivatives in Problems 41-46 algebraically.
41. f(x) = 5x2 at x = 10
43. g(t) = t2 + tatt = -1
Homework 4
In Exercises 19-20, find a formula for the derivative using the
power rule. Confirm it using difference quotients.
19. k(x) = 1/x
20. 1(x) = 1/22
Find a formula for the derivatives of the functions in Exer-
cises 21-22 using difference quotients.
21. g(x) = 2x2 - 3
22. m(x) = 1/(x + 1)

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