Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
Related questions
Question
Question 38
![IT X
26. f(x) — сos
at x :
2
0.5
60
13.2
75
12.5
IT X
90
11.9
27. f(x) = tan
at x
= 0.5
2
105
11.2
120
10.7
IT X
at x = 1
2
28. f(x) = sin
1
at x = 3
Data Source: Arnd Leike, "Demonstration of the
Exponential Decay Law Using Beer Froth," European
Journal Physics 23 (2002): 21–26.
29. f(x) =
x + 3
30. f(x) — е* at x %3D 0
46. The height f(x), in feet, of the tide at time x hours,
where the graph of y = f(x)is provided in Fig-
ure 2.9, over intervals [0.25, 0.50] and [1, 2]
31. f(x) = lnx at x = 9
32. f(x) = tan x at x = 0
33. f(x) = tan
IT X
at x = 0.95
2
y
4
1
34. f(x) = ln – at x = 1
3
35. f(x) = In
1
at x = 0.1
2
36. f(x) = e-* at x = 0
1
Algebraically determine the tangent line for y = f(x)
at the point specified in Problems 37 to 42. Graph both
y = f(x) and the tangent line on the same plot.
0.5
1
1.5
Figure 2.9 Tidal height.
37. f(x) — Зх — 7atx — 3
38. f(x) = x² at x = –1
Approximate the instantaneous rates of change of the
given functions at the points specified in Problems 47 to
50. These are the same functions as those in Problems 43
39. f(x) = 3x² at x = -2
40. f(x) = x³ at x = 1
to 46.
Vx +h+ Vx
Vx +h+ /x
47. P(t) = 8.3(1.33)' is the number (in millions) of peo-
ple living in the United States t decades after 1815 at
the points t = 0 and t = 2.
41. Jx at x =
= 9. Hint: Multiply by
42. V5x at x = 5](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe4db1e84-75df-498d-9686-5cabfd0e0c2f%2F59b58b81-a51d-42fb-b30a-8903bfeb6f13%2F6i4fhqv_processed.jpeg&w=3840&q=75)
Transcribed Image Text:IT X
26. f(x) — сos
at x :
2
0.5
60
13.2
75
12.5
IT X
90
11.9
27. f(x) = tan
at x
= 0.5
2
105
11.2
120
10.7
IT X
at x = 1
2
28. f(x) = sin
1
at x = 3
Data Source: Arnd Leike, "Demonstration of the
Exponential Decay Law Using Beer Froth," European
Journal Physics 23 (2002): 21–26.
29. f(x) =
x + 3
30. f(x) — е* at x %3D 0
46. The height f(x), in feet, of the tide at time x hours,
where the graph of y = f(x)is provided in Fig-
ure 2.9, over intervals [0.25, 0.50] and [1, 2]
31. f(x) = lnx at x = 9
32. f(x) = tan x at x = 0
33. f(x) = tan
IT X
at x = 0.95
2
y
4
1
34. f(x) = ln – at x = 1
3
35. f(x) = In
1
at x = 0.1
2
36. f(x) = e-* at x = 0
1
Algebraically determine the tangent line for y = f(x)
at the point specified in Problems 37 to 42. Graph both
y = f(x) and the tangent line on the same plot.
0.5
1
1.5
Figure 2.9 Tidal height.
37. f(x) — Зх — 7atx — 3
38. f(x) = x² at x = –1
Approximate the instantaneous rates of change of the
given functions at the points specified in Problems 47 to
50. These are the same functions as those in Problems 43
39. f(x) = 3x² at x = -2
40. f(x) = x³ at x = 1
to 46.
Vx +h+ Vx
Vx +h+ /x
47. P(t) = 8.3(1.33)' is the number (in millions) of peo-
ple living in the United States t decades after 1815 at
the points t = 0 and t = 2.
41. Jx at x =
= 9. Hint: Multiply by
42. V5x at x = 5
Expert Solution
Step 1
Solution Question 38
Given,
The curve
We have to find the equation of the tangent at point
Step by step
Solved in 4 steps with 1 images
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