Homework Answers
(10 marks) Let C be the curve 64x – - y3 = 0 between y =...
(10 marks) Let C be the curve 64x – - y3 = 0 between y = 0 and y = 3. Sketch the graph of this curve. In each part, set up, but do not evaluate, an integral or a sum of integrals that solves the problem. (a) Find the area of the surface generated by revolving C about the x-axis by integrating with respect to x. (b) Find the area of the surface generated by revolving C about the...
(9 marks) Let { ln(n+11) n+3 }n=1 be a sequence. a. Find the first 5 terms...
(9 marks) Let { ln(n+11) n+3 }n=1 be a sequence. a. Find the first 5 terms of the sequence in the exact form. b. Determine whether the sequence is strictly monotone, monotone, eventually strictly monotone, eventually monotone or neither. Prove it. c. Determine whether the sequence is convergent, and if so, find its limit.
r-a- asin 0, y= a- acose (0s 0s 2m , a> 0 ) represent one arc of a cycloid. Find 18. The equation the surface ar...
r-a- asin 0, y= a- acose (0s 0s 2m , a> 0 ) represent one arc of a cycloid. Find 18. The equation the surface area generated by revolving this curve about the -axis. 2 and a+1 is convergent or divergent. 2+ a 19. Determine whether the sequence satisfying a If it converges, find the limit.
r-a- asin 0, y= a- acose (0s 0s 2m , a> 0 ) represent one arc of a cycloid. Find 18. The equation the...
Let C be the portion of the curve rve y = x3 + 3x – 1...
Let C be the portion of the curve rve y = x3 + 3x – 1 between the points (1, 3) and (2, 13). (a) Write down a definite integral for the arclength of C. Do not evaluate the integral. (b) Write down a definite integral for the surface area of the surface of revolution obtained by revolving Cabout the x-axis. Do not evaluate the integral. (c) Write down a definite integral for the surface area of the surface of...
8. Use the shell method to set up and evaluate the integral y- 3x that gives the volume of the solid generated by revolving the plane region about the y-axis. a. 192R b. 384x C. 192x d. 384x e. 9...
8. Use the shell method to set up and evaluate the integral y- 3x that gives the volume of the solid generated by revolving the plane region about the y-axis. a. 192R b. 384x C. 192x d. 384x e. 96x 7 9. Set up and evaluate the definite integral for the area of the surface formed by revolving graph of y-9-2 about the y-axis. Round your answer to three decimal places.
8. Use the shell method to set up and...
a. Set up an integral for the area of the surface generated by revolving the curve...
a. Set up an integral for the area of the surface generated by revolving the curve x = 3 sin y, 0 sys about the y-axis. b. Graph the curve. c. Use technology to find the surface area numerically.
a. Set up an integral for the area of the surface generated by revolving the curve x = 3 sin y, 0 sys about the y-axis. b. Graph the curve. c. Use technology to find the surface area numerically.
Assignment 4: (Arc Length and Surface Area - 7.3) 1. Consider the plane curve C defined...
Assignment 4: (Arc Length and Surface Area - 7.3) 1. Consider the plane curve C defined by y=e" between y-1 and y-e. (a.) Set up, but do NOT evaluate, an integral with respect to y for the arc length of C. (b.) Set up, but do NOT evaluate, an integral with respect to x for the arc length of C. Set up, but do NOT evaluate, an integral for the area of the surface obtained by rotating C about the...
Q.1 A. Compute each of the following integrals. 0 s V7(5x+3)+ te dv.(2 Marks) (1) Sax...
Q.1 A. Compute each of the following integrals. 0 s V7(5x+3)+ te dv.(2 Marks) (1) Sax 24.dx. (3 Marks) B. (1) Evaluate dx. (3 Marks) (ii) Find the volume generated by revolving the curve y = sin x and y = 0 in 0 SXS ,about the x-axis.(2 Marks)
1. For the curve defined by y=725 - r from x = 0 to x =...
1. For the curve defined by y=725 - r from x = 0 to x = 4 Set-up the integral that finds the length of the arc formed by the curve. You do not need to simplify the expression undemeath the radical. Do not integrate! b. [6 pts) Set-up the integral that finds the surface area of the solid generated by revolving the curve about the x-axis, You do not need to simplify the expression underneath the radical. Do not...
Check Choose Section 7.4 pt 2 Practice Find the surface area of the surface generated by revolving y-9- and y-o fro...
Check Choose Section 7.4 pt 2 Practice Find the surface area of the surface generated by revolving y-9- and y-o from x- -2 and x 2 about the x- axis. Find the exact answer showing all calculus work. 1. Choos "Chech and y-0 from 2. Find the surface area of the surface generated by revolving y- x0 andx2 about the x - axis. Use your calculator and round to the hundredth place. 3. Find the surface area of the surface...
(10 marks) Let C be the curve 64x – - y3 = 0 between y = 0 and y = 3. Sketch the graph of this curve. In each part, set up, but do not evaluate, an integral or a sum of integrals that solves the problem. (a) Find the area of the surface generated by revolving C about the x-axis by integrating with respect to x. (b) Find the area of the surface generated by revolving C about the...
(9 marks) Let { ln(n+11) n+3 }n=1 be a sequence. a. Find the first 5 terms of the sequence in the exact form. b. Determine whether the sequence is strictly monotone, monotone, eventually strictly monotone, eventually monotone or neither. Prove it. c. Determine whether the sequence is convergent, and if so, find its limit.
r-a- asin 0, y= a- acose (0s 0s 2m , a> 0 ) represent one arc of a cycloid. Find 18. The equation the surface area generated by revolving this curve about the -axis. 2 and a+1 is convergent or divergent. 2+ a 19. Determine whether the sequence satisfying a If it converges, find the limit.
r-a- asin 0, y= a- acose (0s 0s 2m , a> 0 ) represent one arc of a cycloid. Find 18. The equation the...
Let C be the portion of the curve rve y = x3 + 3x – 1 between the points (1, 3) and (2, 13). (a) Write down a definite integral for the arclength of C. Do not evaluate the integral. (b) Write down a definite integral for the surface area of the surface of revolution obtained by revolving Cabout the x-axis. Do not evaluate the integral. (c) Write down a definite integral for the surface area of the surface of...
8. Use the shell method to set up and evaluate the integral y- 3x that gives the volume of the solid generated by revolving the plane region about the y-axis. a. 192R b. 384x C. 192x d. 384x e. 96x 7 9. Set up and evaluate the definite integral for the area of the surface formed by revolving graph of y-9-2 about the y-axis. Round your answer to three decimal places.
8. Use the shell method to set up and...
a. Set up an integral for the area of the surface generated by revolving the curve x = 3 sin y, 0 sys about the y-axis. b. Graph the curve. c. Use technology to find the surface area numerically.
a. Set up an integral for the area of the surface generated by revolving the curve x = 3 sin y, 0 sys about the y-axis. b. Graph the curve. c. Use technology to find the surface area numerically.
Assignment 4: (Arc Length and Surface Area - 7.3) 1. Consider the plane curve C defined by y=e" between y-1 and y-e. (a.) Set up, but do NOT evaluate, an integral with respect to y for the arc length of C. (b.) Set up, but do NOT evaluate, an integral with respect to x for the arc length of C. Set up, but do NOT evaluate, an integral for the area of the surface obtained by rotating C about the...
Q.1 A. Compute each of the following integrals. 0 s V7(5x+3)+ te dv.(2 Marks) (1) Sax 24.dx. (3 Marks) B. (1) Evaluate dx. (3 Marks) (ii) Find the volume generated by revolving the curve y = sin x and y = 0 in 0 SXS ,about the x-axis.(2 Marks)
1. For the curve defined by y=725 - r from x = 0 to x = 4 Set-up the integral that finds the length of the arc formed by the curve. You do not need to simplify the expression undemeath the radical. Do not integrate! b. [6 pts) Set-up the integral that finds the surface area of the solid generated by revolving the curve about the x-axis, You do not need to simplify the expression underneath the radical. Do not...
Check Choose Section 7.4 pt 2 Practice Find the surface area of the surface generated by revolving y-9- and y-o from x- -2 and x 2 about the x- axis. Find the exact answer showing all calculus work. 1. Choos "Chech and y-0 from 2. Find the surface area of the surface generated by revolving y- x0 andx2 about the x - axis. Use your calculator and round to the hundredth place. 3. Find the surface area of the surface...
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