Other
Calculus early transcendentals 10th edition solutions
- Course
- Institution
- Book
This document contains the solutions of calculus early transcendentals 10th edition . Very useful for students studying calculus.
[Show more]
Connected book
Book Title:
Author(s):
- Edition:
- ISBN:
- Edition:
More summaries for
-
Solution Manual for Calculus Early Transcendentals 10th edition by Anton,Bivens,Davis A+
-
Solution Manual for Calculus Early Transcendentals 10th edition by Anton,Bivens,Davis|Complete
-
Solution Manual for Calculus Early Transcendentals 10th edition by Anton,Bivens,Davis|Complete
Seller
Follow
gowthamys
Content preview
INSTRUCTORSOLUTIONS
MANUAL
, Contents
Chapter 0. Before Calculus .. 1
Chapter 1. Limits and Continuity .. 39
Chapter 2. The Derivative .. .71
Chapter 3. Topics in Differentiation .. 109
Chapter 4. The Derivative in Graphing and Applications .. 153
Chapter 5. Integration .. 243
Chapter 6. Applications of the Definite Integral in Geometry Science and Engineering 305
Chapter 7. Principals of Integral Evaluation .. 363
Chapter 8. Mathematical Modeling with Differential Equations 413
Chapter 9. Infinite Series .. 437
Chapter 10. Parametric and Polar Curves; Conic Sections . 485
Chapter 11. Three-Dimensional Space Vectors . 545
Chapter 12. Vector-Valued Functions . 589
Chapter 13. Partial Derivatives . 627
Chapter 14. Multiple Integrals 675
Chapter 15. Topics in Vector Calculus . .. 713
Appendix A. Graphing Functions Using Calculators and Computer Algebra Systems . . 745
Appendix B. Trigonometry Review .. 753
Appendix C. Solving Polynomial Equations 759
,Before Calculus
Exercise Set 0.1
1. (a) −2.9, −2.0, 2.35, 2.9 (b) None (c) y = 0 (d) −1.75 ≤ x ≤ 2.15, x = −3, x = 3
(e) ymax = 2.8 at x = −2.6; ymin = −2.2 at x = 1.2
2. (a) x = −1, 4 (b) None (c) y = −1 (d) x = 0, 3, 5
(e) ymax = 9 at x = 6; ymin = −2 at x = 0
3. (a) Yes (b) Yes (c) No (vertical line test fails) (d) No (vertical line test fails)
4. (a) The natural domain of f is x 6= −1, and for g it is the set of all x. f (x) = g(x) on the intersection of their
domains.
(b) The domain of f is the set of all x ≥ 0; the domain of g is the same, and f (x) = g(x).
5. (a) 1999, $47,700 (b) 1993, $41,600
(c) The slope between 2000 and 2001 is steeper than the slope between 2001 and 2002, so the median income was
declining more rapidly during the first year of the 2-year period.
47.7 − 41.6 6.1
6. (a) In thousands, approximately = per yr, or $1017/yr.
6 6
(b) From 1993 to 1996 the median income increased from $41.6K to $44K (K for ‘kilodollars’; all figures approx-
imate); the average rate of increase during this time was (44 − 41.6)/3 K/yr = 2.4/3 K/yr = $800/year. From
1996 to 1999 the average rate of increase was (47.7 − 44)/3 K/yr = 3.7/3 K/yr ≈ $1233/year. The increase was
larger during the last 3 years of the period.
(c) 1994 and 2005.
2 2 2 2
√
√ f2(0) = 3(0) − 2 = −2; f2 (2) = 3(2)2 − 2 = 10; f (−2) = 3(−2) − 2 = 10; f (3) = 3(3) − 2 = 25; f ( 2) =
7. (a)
3( 2) − 2 = 4; f (3t) = 3(3t) − 2 = 27t − 2.
√ √
(b) f (0) = 2(0) = 0; f (2) = 2(2) = 4; f (−2) = 2(−2) = −4; f (3) = 2(3) = 6; f ( 2) = 2 2; f (3t) = 1/(3t) for
t > 1 and f (3t) = 6t for t ≤ 1.
3+1 −1 + 1 π+1 −1.1 + 1 −0.1 1
8. (a) g(3) = = 2; g(−1) = = 0; g(π) = ; g(−1.1) = = = ; g(t2 − 1) =
3−1 −1 − 1 π−1 −1.1 − 1 −2.1 21
t2 − 1 + 1 t2
2
= 2 .
t −1−1 t −2
√ √
(b) g(3) = 3 + 1 = 2; g(−1) = 3; g(π) = π + 1; g(−1.1) = 3; g(t2 − 1) = 3 if t2 < 2 and g(t2 − 1) =
√
t2 − 1 + 1 = |t| if t2 ≥ 2.
1
, 2 Chapter 0
9. (a) Natural domain: x 6= 3. Range: y 6= 0. (b) Natural domain: x 6= 0. Range: {1, −1}.
√ √
(c) Natural domain: x ≤ − 3 or x ≥ 3. Range: y ≥ 0.
√
(d) x2 − 2x + 5 = (x − 1)2 + 4 ≥ 4. So G(x) is defined for all x, and is ≥ 4 = 2. Natural domain: all x. Range:
y ≥ 2.
(e) Natural domain: sin x 6= 1, so x 6= (2n+ 21 )π, n = 0, ±1, ±2, . . .. For such x, −1 ≤ sin x < 1, so 0 < 1−sin x ≤ 2,
1 1 1
and 1−sin x ≥ 2 . Range: y ≥ 2 .
2
(f ) Division by 0 occurs for x = 2. For all other x, xx−2
−4
= x + 2, which is nonnegative for x ≥ −2. Natural
√ √
domain: [−2, 2) ∪ (2, +∞). The range of x + 2 is [0, +∞). But we must exclude x = 2, for which x + 2 = 2.
Range: [0, 2) ∪ (2, +∞).
10. (a) Natural domain: x ≤ 3. Range: y ≥ 0. (b) Natural domain: −2 ≤ x ≤ 2. Range: 0 ≤ y ≤ 2.
(c) Natural domain: x ≥ 0. Range: y ≥ 3. (d) Natural domain: all x. Range: all y.
(e) Natural domain: all x. Range: −3 ≤ y ≤ 3.
√ √
(f ) For x to exist, we must have x ≥ 0. For H(x) to exist, we must also have sin x 6= 0, which is equivalent
√ √ to
x 6= πn√for n = 0, 1, 2, . . .. Natural domain: x > 0, x 6= (πn)2 for n = 1, 2, . . .. For such x, 0 < | sin x| ≤ 1, so
0 < (sin x)2 ≤ 1 and H(x) ≥ 1. Range: y ≥ 1.
11. (a) The curve is broken whenever someone is born or someone dies.
(b) C decreases for eight hours, increases rapidly (but continuously), and then repeats.
12. (a) Yes. The temperature may change quickly under some conditions, but not instantaneously.
(b) No; the number is always an integer, so the changes are in movements (jumps) of at least one unit.
h
t
13.
T
t
14.
√
15. Yes. y = 25 − x2 .
√
16. Yes. y = − 25 − x2 .
√
2
17. Yes. y = √25 − x , −5 ≤ x ≤ 0
− 25 − x2 , 0<x≤5
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through EFT, credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying this summary from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller gowthamys. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy this summary for R132,05. You're not tied to anything after your purchase.
Can Stuvia be trusted?
4.6 stars on Google & Trustpilot (+1000 reviews)
76669 documents were sold in the last 30 days
Founded in 2010, the go-to place to buy summaries for 14 years now