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Unformatted text preview: $15,000 and $20,000 (D) between $20,000 and $25,000 (E) more than $25,000 44. Christine O’Brien, who is selfemployed, wants to invest $80,000 in a pension plan. One investment
oﬀers 6% compounded quarterly. Another oﬀers 5.75% compounded continuously.
(i) Which investment will earn the most interest in 4 years? (ii) How much more will the better plan earn? (iii) What is the eﬀective rate in each case? (iv) If Ms. O’Brien chooses the plan with continuous compounding, how long will it take for her
$80,000 to grow to $90,000? 45. Sales of a new model of compact disc player are approximated by the function
S (x) = 1100 − 800e−x ,
where S (x) is in appropriate units and x represents the number of years the disc player has been on
the market
(i) Find the sales during year 0. (ii) In how many years will sales reach 900 units? (iii) Will sales ever reach 1,100 units? (iv) Is there a limit on sales for this product? If so, what is it? 46. Use the table of values to estimate lim f (x).
x→7 x 6.9 6.99 6.999 6.9999 7.0001 7.001 7.01 7.1 f ( x) 9.9 9.99 9.999 9.9999 10.0001 10.001 10.01 10.1 (A) 7 (B) 10 (C) 9.9 (D) 10.1 (E) the limit does not exist 47. Suppose lim f (x) = 9, and lim f (x) = 9, but f (5) does not exist. What can you say about lim f (x)?
x → 5− x→5 x → 5+ (A) lim f (x) = 9 (B) lim f (x) = −9 (D) lim f (x) = ∞ (E) None of these x→ 5 x→5 x→5 (C) lim f (x) does not exist
x→5 48. The graph of f (x) is given below. Use the graph to ﬁnd lim f (x).
x→3 (A) 4 (B) 3 (C) 3.5 (D) 0 (E) the limit does not exist 49. Let f (x) = x2 − 1
. Answer parts (i) through (iii)
x+1 (i) Complete the table below.
x 1.1 1.01 1.001 0.999 0.99 0.9 x2 − 1
x+1 x2 − 1
.
x→−1 x + 1 (ii) Use the table to calculate lim
(A) 2 (B) 1 (C) ∞ (D) 2 (E) the limit does not exist (iii) Verify your answer by using a graphing calculator. Choose the correct graph below. The graph
below is displayed on a [−4, 4, 1] by [−4, 4, 1] window. 50. Use the graph of f (x) = ex below to ﬁnd lim ex .
x→−∞ (A) lim ex = e (B) lim ex does not exist (D) lim ex = 0 (E) None of these x→−∞ x→−∞ 51. Find lim x→∞ x→−∞ (C) lim ex = ∞
x→−∞ 3
.
2x − 1
(A) lim 3
3
=
2x − 1
2 (D) lim 3
=0
2x − 1 x→∞ x→∞ (B) lim x→∞ 3
does not exist
2x − 1 (E) None of these (C) lim x→∞ 3
=∞
2x − 1 52. Let f (x) = 7x3 + 7. Answer parts (i) through (iii)
(i) Find the average rate of change of the function f (x) = 7x3 + 7 over the interval [5, 7].
The average rate of change is
(A) less than 600 (B) between 600 and 650 (D) between 700 and 750 (C) between 650 and 700 (E) more than 750 (ii) Find the average rate of change of the function f (x) = 7x3 + 7 over the interval [−1, 1].
The average rate of change is
(A) less than 10 (B) between 10 and 0 (D) between 10 and 20 (C) between 0 and 10 (E) more than 20 (iii) Find the instantaneous rate of change of the function f (x) = 7x3 + 7 at x = 5.
The instananeous rate of change is
(A) less than 600 (...
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This note was uploaded on 01/14/2014 for the course MATH 116 taught by Professor Jess during the Fall '09 term at University of Arizona Tucson.
 Fall '09
 JESS
 Calculus, Slope

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