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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![1. (a) Use the Wallis sine formula to evaluate ( sin* xdx.
(b) Evaluate [
1
- dx by using properties of improper integrals.
(x–2)²/
2. (a) Find the exact surface area that is generated by revolving the portion of the curve
y = x' between x=1 and x = 2 about the y-axis. Sketch the generated surface.
(b) Find the exact arc length of the curve
x= e" (sin t + cost), y =e" (sin t – cost)
over the interval [-1, 1].
dy
3. (a) If y=x* tanh'(Vx)+ Je** +cosh’(5x), find
dx
(b) Sketch the polar curve r= 4cos 20 and r = 2/2. Then find the area of the region that
is inside the rose curve r=4cos20 and outside the circle r= 2/2. Sketch the region.
4. (a) Derive the equation of the parabola x² = 4py.
(b) The equation of an ellipse is given by 9.x² +4y² –18x+24y+9=0. Sketch the ellipse
and then label the center, vertices, foci and ends of the minor axis.
16
5. (a) Find the constants a,b,c for the conic r =
Sketch the conic.
5– 3cos0
3
(b) Given r
Find the distances from the pole to the vertices and then find the
2+ sin 0*
equation of the conic in rectangular coordinates. Sketch the conic.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F04a5ce0c-deab-4888-8161-065b569ec992%2Fc69469f8-8caa-4640-83cd-a67126f34492%2F3ln82xq_processed.png&w=3840&q=75)
Transcribed Image Text:1. (a) Use the Wallis sine formula to evaluate ( sin* xdx.
(b) Evaluate [
1
- dx by using properties of improper integrals.
(x–2)²/
2. (a) Find the exact surface area that is generated by revolving the portion of the curve
y = x' between x=1 and x = 2 about the y-axis. Sketch the generated surface.
(b) Find the exact arc length of the curve
x= e" (sin t + cost), y =e" (sin t – cost)
over the interval [-1, 1].
dy
3. (a) If y=x* tanh'(Vx)+ Je** +cosh’(5x), find
dx
(b) Sketch the polar curve r= 4cos 20 and r = 2/2. Then find the area of the region that
is inside the rose curve r=4cos20 and outside the circle r= 2/2. Sketch the region.
4. (a) Derive the equation of the parabola x² = 4py.
(b) The equation of an ellipse is given by 9.x² +4y² –18x+24y+9=0. Sketch the ellipse
and then label the center, vertices, foci and ends of the minor axis.
16
5. (a) Find the constants a,b,c for the conic r =
Sketch the conic.
5– 3cos0
3
(b) Given r
Find the distances from the pole to the vertices and then find the
2+ sin 0*
equation of the conic in rectangular coordinates. Sketch the conic.
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