CALCULUS: EARLY TRANS. (LL)W/WEBASSIGN
8th Edition
ISBN: 9780357019788
Author: Stewart
Publisher: CENGAGE L
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Chapter A, Problem 69E
To determine
To show: The sum, difference and the product of rational numbers is again a rational number.
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3. f(7)
3. Find the domain of each of the following functions.
1
1. f(x)=2-6x+8
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4. A manufacturer has a monthly fixed cost of $40,000 and a production cost of $8 for each unit produced. The product sells for $12
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7. Evaluate the following limits and justify each step.
(a) lim (3x²+2x+1)
1
x²+4x-12
(b) lim
1 2
x² - 2x
t-√√3t+4
(c) lim
t-0 4-t
x²-6x+5
(d) lim
(e) lim
x 5 x-5
x→2
x²+2x+3
4u+1-3
(f) lim
u➡2 u-2
1
(g) lim
x-3
2
x 55 x
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7x4 +4
(h) lim
xx 5x+2x-1
x+1
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6. Given the following graph f(x).
(-2,2)
2-
-5
-3 -2
(-2,-1)
-1
(0,1)
-2-
1
(3,0)
2 3 4 5
(3,-1)
א
X
Compute each of the following.
(a) f(-2)
(b) lim f(x)
#129
(c) lim f(x)
*→12+
(d) lim f(x)
811H
(e) f(0)
(f) lim f(x)
8011
(m) Is the function continuous at x = -2,0,3? Why or why not?
(g) lim f(x)
+0x
(h) lim f(x)
x 0
(i) f(3)
(j) lim f(x)
x-3-
(k) lim f(x)
x+3+
(1) lim f(x)
#13
Chapter A Solutions
CALCULUS: EARLY TRANS. (LL)W/WEBASSIGN
Ch. A - Prob. 1ECh. A - Prob. 2ECh. A - Prob. 3ECh. A - Prob. 4ECh. A - Rewrite the expression without using the...Ch. A - Prob. 6ECh. A - Prob. 7ECh. A - Prob. 8ECh. A - Rewrite the expression without using the...Ch. A - Prob. 10E
Ch. A - Prob. 11ECh. A - Prob. 12ECh. A - Prob. 13ECh. A - Prob. 14ECh. A - Prob. 15ECh. A - Prob. 16ECh. A - Prob. 17ECh. A - Prob. 18ECh. A - Prob. 19ECh. A - Prob. 20ECh. A - Prob. 21ECh. A - Prob. 22ECh. A - Prob. 23ECh. A - Prob. 24ECh. A - Prob. 25ECh. A - Prob. 26ECh. A - Prob. 27ECh. A - Prob. 28ECh. A - Prob. 29ECh. A - Prob. 30ECh. A - Prob. 31ECh. A - Solve the inequality in terms of intervals and...Ch. A - Prob. 33ECh. A - Prob. 34ECh. A - Prob. 35ECh. A - Prob. 36ECh. A - Prob. 37ECh. A - Prob. 38ECh. A - The relationship between the Celsius and...Ch. A - Prob. 40ECh. A - As dry air moves upward, it expands and in so...Ch. A - Prob. 42ECh. A - Prob. 43ECh. A - Prob. 44ECh. A - Prob. 45ECh. A - Prob. 46ECh. A - Prob. 47ECh. A - Prob. 48ECh. A - Prob. 49ECh. A - Prob. 50ECh. A - Prob. 51ECh. A - Prob. 52ECh. A - Prob. 53ECh. A - Prob. 54ECh. A - Prob. 55ECh. A - Prob. 56ECh. A - Prob. 57ECh. A - Solve for x, assuming a, b, and c are positive...Ch. A - Prob. 59ECh. A - Prob. 60ECh. A - Prob. 61ECh. A - Prob. 62ECh. A - Prob. 63ECh. A - Prob. 64ECh. A - Prob. 65ECh. A - Prob. 66ECh. A - Prob. 67ECh. A - Prob. 68ECh. A - Prob. 69ECh. A - (a) Is the sum of two irrational numbers always an...
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- 3. Compute the profit corresponding to 12,000 units. 5. A rectangular box is to have a square base and a volume of 20 ft3. The material for the base costs $0.30 per ft2, the material for the sides cost $0.10 per ft2, and the material for the top costs $0.20 per ft2. Letting a denote the length of one side of the base, find a function in the variable x giving the cost of constructing the box. 6. Given the following graph f(x).arrow_forward8. On what intervals, each function continuous? (a) f(x) = 3x11 + 4x²+1 3x²+5x-1 (b) g(x) = x²-4 X, x < 1, QTs the function f(x) continuous at = 1? Use the definition of continuity to justifyarrow_forwardreview problem please help!arrow_forward
- 3. Consider the sequences of functions f₁: [-π, π] → R, sin(n²x) An(2) n f pointwise as (i) Find a function ƒ : [-T,π] → R such that fn n∞. Further, show that fn →f uniformly on [-π,π] as n → ∞. [20 Marks] (ii) Does the sequence of derivatives f(x) has a pointwise limit on [-7, 7]? Justify your answer. [10 Marks]arrow_forward1. (i) Give the definition of a metric on a set X. [5 Marks] (ii) Let X = {a, b, c} and let a function d : XxX → [0, ∞) be defined as d(a, a) = d(b,b) = d(c, c) 0, d(a, c) = d(c, a) 1, d(a, b) = d(b, a) = 4, d(b, c) = d(c,b) = 2. Decide whether d is a metric on X. Justify your answer. = (iii) Consider a metric space (R, d.), where = [10 Marks] 0 if x = y, d* (x, y) 5 if xy. In the metric space (R, d*), describe: (a) open ball B2(0) of radius 2 centred at 0; (b) closed ball B5(0) of radius 5 centred at 0; (c) sphere S10 (0) of radius 10 centred at 0. [5 Marks] [5 Marks] [5 Marks]arrow_forward(c) sphere S10 (0) of radius 10 centred at 0. [5 Marks] 2. Let C([a, b]) be the metric space of continuous functions on the interval [a, b] with the metric doo (f,g) = max f(x)g(x)|. xЄ[a,b] = 1x. Find: Let f(x) = 1 - x² and g(x): (i) do(f, g) in C'([0, 1]); (ii) do(f,g) in C([−1, 1]). [20 Marks] [20 Marks]arrow_forward
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