Exam (elaborations)

Solutions for Calculus & Its Applications, 15th Edition Goldstein (All Chapters included)

66 views 2 purchases

Course
Calculus

Institution
Calculus

Complete Solutions Manual for Calculus & Its Applications, 15th Edition by Larry J. Goldstein, David Lay, Nakhle I Asmar, David I. Schneider ; ISBN13: 9780137590612. (Full Chapters included Chapter 1 to 12)....0.Functions 1.The Derivative 2.Applications of the Derivative 3.Techniques of Differen...

[Show more]

Preview 4 out of 400 pages

View example

Uploaded on May 10, 2024
Number of pages 400
Written in 2023/2024
Type Exam (elaborations)
Contains Questions & answers

solutions
manual
solutions manaul
answer guide
end of chapter
calculus
applications
15th edition
15e
goldstein
9780137590612

Institution Calculus
Course Calculus

mizhouubcca

Member since 1 year 749 documents sold

CA$43.67

Add to cart

Add to wishlist

100% satisfaction guarantee
Immediately available after payment
Both online and in PDF
No strings attached

INSTRUCTOR’S
SOLUTIONS MANUAL

C ALCULUS AND I TS A PPLICATIONS
FIFTEENTH EDITION

C ALCULUS AND I TS A PPLICATIONS ,
B RIEF V ERSION
FIFTEENTH EDITION

Larry J. Goldstein
Goldstein Educational Technologies

David C. Lay
University of Maryland

David I. Schneider
University of Maryland

Nakhlé H. Asmar
University of Missouri

** Immediate Download
** Swift Response
** All Chapters included

, CONTENTS

Chapter 0 Functions .............................................................................................1
Chapter 1 The Derivative ..................................................................................26
Chapter 2 Applications of the Derivative ..........................................................73
Chapter 3 Techniques of Differentiation .........................................................121
Chapter 4 The Exponential and Natural Logarithmic Functions .....................147
Chapter 5 Applications of the Exponential and Natural Logarithm
Functions .........................................................................................177
Chapter 6 The Definite Integral .......................................................................196
Chapter 7 Functions of Several Variables .......................................................230
Chapter 8 The Trigonometric Functions .........................................................267
Chapter 9 Techniques of Integration ...............................................................286
Chapter 10 Differential Equations .....................................................................327
Chapter 11 Taylor Polynomials and Infinite Series...........................................360
Chapter 12 Probability and Calculus .................................................................382

, Chapter 0 Functions
0.1 Functions and Their Graphs 16. h( s ) =
s
1. (1 + s )
1 1
⎛1⎞ 1
h⎜ ⎟ = 2 = 2
=
2. ⎝ 2 ⎠ 1+ 1
2 ( ) 3
2
3
3. ⎛ 3⎞ − 32 −3
h ⎜− ⎟ = = 12 = 3
4.
⎝ 2 ⎠ 1+ − 3 −2 ( 2)
a +1 a +1
h(a + 1) = =
5. 1 + (a + 1) a + 2

6. 17. f ( x) = 3 x + 2, h ≠ 0
f (3 + h ) = 3 (3 + h ) + 2 = 9 + 3h + 2 = 3h + 11
⎛ 3⎞ f (3) = 3 (3) + 2 = 11
7. [2, 3) 8. ⎜ −1, ⎟
⎝ 2⎠
f (3 + h ) − f (3) (3h + 11) − 11 3h
9. [–1, 0) 10. [–1, 8) = = =3
h h h
11. (−∞, 3) 12. ⎡⎣ 2, ∞ ) 18. f ( x) = x 2 , h ≠ 0
f (1 + h ) = (1 + h ) = 1 + 2h + h 2
2
13. f ( x) = x 2 − 3 x
f (1) = 12 = 1
f (0) = 0 2 − 3(0) = 0
f (5) = 5 2 − 3(5) = 25 − 15 = 10 ( 2
f (1 + h ) − f (1) 1 + 2h + h − 1
=
)
h h
f (3) = 3 2 − 3(3) = 9 − 9 = 0
2h + h 2
= = 2+h
f (−7) = (−7) 2 − 3(−7) = 49 + 21 = 70 h

14. f ( x) = x 3 + x 2 − x − 1 19. a. k ( x ) = x + 273
3 2 5933 = x + 273 ⇒ x = 5660
f (1) = 1 + 1 − 1 − 1 = 0
The boiling point of tungsten is 5660°C.
f (−1) = (−1) 3 + (−1) 2 − (−1) − 1 = 0
9
3 2 b. f ( x) = x + 32
⎛1⎞ ⎛1⎞ ⎛1⎞ ⎛1⎞ 9 5
f ⎜ ⎟ = ⎜ ⎟ + ⎜ ⎟ − ⎜ ⎟ −1 = −
⎝2⎠ ⎝2⎠ ⎝2⎠ ⎝2⎠ 8 9
f ( x ) = (5660) + 32 = 10220
5
f (a) = a 3 + a 2 − a − 1
The boiling point of tungsten is 10220°F.
15. f ( x) = x 2 − 2 x 20. a. f (0) represents the number of laptops sold
2 in 2015.
f (a + 1) = (a + 1) − 2(a + 1)
= (a 2 + 2a + 1) − 2a − 2 = a 2 − 1 b. f (5) = 150 + 2(5) + 5 2
f (a + 2) = (a + 2) 2 − 2(a + 2) = 150 + 10 + 25 = 185
In 2020, the company will sell 185
= (a 2 + 4a + 4) − 2a − 4 = a 2 + 2a laptops.
8x
21. f ( x) =
( x − 1)( x − 2)
all real numbers such that x ≠ 1, 2 or
(−∞, −1)  (−1, 2)  (2, ∞ )

1

, 2 Chapter 0 Functions

1 37. positive 38. negative
22. f (t ) =
t 39. [−1, 3] 40. −1, 5, 9
all real numbers such that t > 0 or (0, ∞ )
41. (−∞, − 1]  [5, 9] 42. [ −1, 5]  [9, ∞ ]
1
23. g ( x ) = 43. f (1) ≈ .03; f (5) ≈ .037
3− x
all real numbers such that x < 3 or ( −∞, −3) 44. f (6) ≈ .03

24. g ( x) =
4 45. [0, .05] 46. t ≈ 3
x ( x + 2)
⎛ 1⎞
all real numbers such that x ≠ 0, –2 or 47. f ( x) = ⎜ x − ⎟ ( x + 2)
⎝ 2⎠
(−∞, −2)  (−2, 0)  (0, ∞ )
⎛ 1⎞ 25
25. f (3) = ⎜ 3 − ⎟ (3 + 2) =
⎝ 2 ⎠ 2
No, (3, 12) is not on the graph.
48. f(x) = x(5 + x)(4 – x)
f(–2) = –2(5 + (–2))(4 – (–2)) = –36
No, (–2, 12) is not on the graph.
3x − 1
26. 49. g ( x) =
x2 + 1
3 (1) − 1 2
g (1) = = =1
(1) 2
+1 2
Yes, (1, 1) is on the graph.

x2 + 4
50. g ( x) =
x+2
27.
( 4) 2 + 4 20 10
g ( 4) = = =
4+2 6 3
⎛ 1⎞
No, ⎜ 4, ⎟ is not on the graph.
⎝ 4⎠

51. f ( x) = x 3
28. f (a + 1) = (a + 1) 3

⎛5⎞
52. f ( x) = ⎜ ⎟ − x
⎝x⎠
5
f (2 + h) = − (2 + h)
(2 + h)
5 − (2 + h) 2 1 − 4h − h 2
= =
29. function 30. not a function (2 + h) 2+h

31. not a function 32. not a function ⎪⎧ x for 0 ≤ x < 2
53. f ( x) = ⎨
33. not a function 34. function ⎪⎩1 + x for 2 ≤ x ≤ 5
35. f (0) = 1; f (7 ) = −1 f (1) = 1 = 1
f (2) = 1 + 2 = 3
36. f ( 2) = 3; f ( −1) = 0 f (3) = 1 + 3 = 4

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 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 these notes from?

Stuvia is a marketplace, so you are not buying this document from us, but from seller mizhouubcca. Stuvia facilitates payment to the seller.

Will I be stuck with a subscription?

No, you only buy these notes for CA$43.67. You're not tied to anything after your purchase.

Can Stuvia be trusted?

4.6 stars on Google & Trustpilot (+1000 reviews)

53068 documents were sold in the last 30 days

Founded in 2010, the go-to place to buy study notes for 14 years now

Start selling

Exam (elaborations)

Solutions for Calculus & Its Applications, 15th Edition Goldstein (All Chapters included)

Document information

Subjects

Written for

Seller

Reviews received

Content preview