For the following exercises, find the lengths of the functions of x over the given interval. Write your result as an exact number. 171. y=x3/2 from (0, 0) to (1, 1)
For the following exercises, find the lengths of the functions of x over the given interval. Write your result as an exact number. 171. y=x3/2 from (0, 0) to (1, 1)
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...
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2.4 CACRCISES
For the following exercises, find the length of the functions
over the given interval.
165. y = 5x from x =
= 0 to x = 2
166. y =
167. x = 4y from y = -1 to y = 1
168. Pick an arbitrary linear function x = g(y) over any
interval of your choice (y₁, y2). Determine the length of
the function and then prove the length is correct by using
geometry.
-x+
1x + 25 from x = 1 to x = 4
169. Find the surface area of the volume generated when
the curve y = √x revolves around the x-axis from (1, 1)
to (4, 2), as seen here.
2
1
E
174.
Page <
2/3
172. y=x² from (1, 1) to (8, 4)
For the following exercises, find the lengths of the
functions of x over the given interval. Write your result as
an exact number.
3/2
171. y=x from (0, 0) to (1, 1)
3/2
173. y=(x²+2) from x = 0 to x = 1
176. y =
3/2
y = (x² − 2)³²2 from x = 2 to x = 4
175. [T] y=e* on x = 0 to x = 1
4
177. = +
178. y =
PortalGuard Sir X
1
2
8x²
3
1
+ from x = 1 to x = 3
3 4x
> of 5
2x³/12 x122
3
from x = 1 to x = 2
3/2
179. y=¹(9x²+6)
27
from x = 1 to x = 4
from x = 0 to x = 2
71°F
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Homework - Vol2 - Section 2.4 - Arc Length of a Curve and Surface Area.pdf
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2.4 CACRCISES
For the following exercises, find the length of the functions
over the given interval.
165. y = 5x from x =
= 0 to x = 2
166. y =
167. x = 4y from y = -1 to y = 1
168. Pick an arbitrary linear function x = g(y) over any
interval of your choice (y₁, y2). Determine the length of
the function and then prove the length is correct by using
geometry.
-x+
1x + 25 from x = 1 to x = 4
169. Find the surface area of the volume generated when
the curve y = √x revolves around the x-axis from (1, 1)
to (4, 2), as seen here.
2
1
E
174.
Page <
2/3
172. y=x² from (1, 1) to (8, 4)
For the following exercises, find the lengths of the
functions of x over the given interval. Write your result as
an exact number.
3/2
171. y=x from (0, 0) to (1, 1)
3/2
173. y=(x²+2) from x = 0 to x = 1
176. y =
3/2
y = (x² − 2)³²2 from x = 2 to x = 4
175. [T] y=e* on x = 0 to x = 1
4
177. = +
178. y =
PortalGuard Sir X
1
2
8x²
3
1
+ from x = 1 to x = 3
3 4x
> of 5
2x³/12 x122
3
from x = 1 to x = 2
3/2
179. y=¹(9x²+6)
27
from x = 1 to x = 4
from x = 0 to x = 2
71°F
Homework 4 - X
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