2. S is the surface y 2 = 4(x 2 + z 2 ), y ∈ [0, 2] obtained by rotating the function y = 2x about the y-axis for y ∈ [0...
2. S is the surface y 2 = 4(x 2 + z 2 ), y ∈ [0, 2] obtained by rotating the function y = 2x about the y-axis for y ∈ [0, 2]. Find a suitable parametric representation of the surface S using the cylindrical polar coordinates.
Answer is: 2. r(u, v) = u cos(v)i + 4uj + u sin(v)k , 0 ≤ v < 2π, 0 ≤ u ≤ 1/2.
I am unsure how to work it out however
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2. S is the surface y 2 = 4(x 2 + z 2 ), y ∈ [0, 2] obtained by rotating the function y = 2x about the y-axis for y ∈ [0...
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2. Consider the line segment & the zz-plane given by cone C by rotating the line about the z-axis. fromz 0 to z4. We can then obtain a 2 (a) 4 pts Find a parametric representation r(u, v) for C, including bounds for u and v. (b) (4 pts Calculate and simplify r x rl (c) 3 pts Use a double integral to find the surface area of C
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Find the exact area of the surface obtained by rotating the curve about the x-axis. y...
Find the exact area of the surface obtained by rotating the
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Question 8 (1 mark) Attempt 1 S is the surface y2 36(2+22 A suitable parametric representation of the surface S is: yE(...
Question 8 (1 mark) Attempt 1 S is the surface y2 36(2+22 A suitable parametric representation of the surface S is: yE(0,6] obtained by rotating the function y 60 about the y-axis for yE[0,6]. _ A (s,e) scos0i+6s2j+ssin0k, 0<s<1, 0<e<2r B T(s,0)scosei+ssin@j+6s2k, 0s1, 0e<2m C Ts, scosei+ssin0j+6sk, 0s1, 0<e<2n (s,0) 6s22+scosej+ssin0k, 0<s<1, 0<0<2 O D OE T(s,) 6st+scosGjssin6k, 0s1, 0<e<2T F T(s,e) scos01+6sj+ssin0k, 0<s<1, 0<0< 2T None of these OG
Question 8 (1 mark) Attempt 1 S is the surface...
Question 8 (1 mark) Attempt 4 ye[0,9 S is the surface y 9(r2+22), ye[0,9] A suitable parametric representation of the s...
Question 8 (1 mark) Attempt 4 ye[0,9 S is the surface y 9(r2+22), ye[0,9] A suitable parametric representation of the surface S is 92 aboute the y-axis for obtained by rotating the functiony= r(s,0) scosi+9sj+ssin@k, 0<<s<1, 0<0<2r O A r(s,0)=scos0i+9s2j+ssin0k, 0<s<1, 0<0<2« B T(s,0)=scos0i+ssinej+9s2k, 0<s<1, 0<0<2« r(s,0)=scosi+ssin@j+9sk, 0<s<1, 0<0<2« D r(s,0)=9si+scos@j+ssin0k, 0 <s<1, 0<0<2T E T(s,0)=9s2i+scosej+ssin0k, 0<s<1, 0<0<2 F G None of these.
Question 8 (1 mark) Attempt 4 ye[0,9 S is the surface y 9(r2+22), ye[0,9] A suitable parametric...
Find the exact area of the surface obtained by rotating the curve about the x-axis. y 2x 2 6 1SXS를 플+을- 263 X\ 266
Find the exact area of the surface obtained by rotating the curve about the x-axis. y 2x 2 6 1SXS를 플+을- 263 X\ 266
Let S be the ‘football’ surface formed by rotating the curve y =
0, x = cos z for z ∈ [−π/2, π/2], around the z-axis. Find a
parametrization for S, and compute its surface area. Please answer
in full With full instructions.
Let S be the 'football, surface formed by rotating the curve y = 0, x-cosz for-E-π/2, π/2], around the z-axis. Find a parametrization for S, and compute its surface area 3
Let S be the 'football, surface...
Find the area of the surface obtained by rotating the given curve about the x-axis. x = 20 cos (0), y = 20 sinº (0), 0 <O< 2 Preview
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2. Consider the line segment & the zz-plane given by cone...
2. Find the surface area of the object obtained s 2 about the y-axis. by rotating y: 478x2,15*
2. Evaluate the surface integral [[Fids. (a) F(x, y, z) - xi + yj + 2zk, S is the part of the paraboloid z - x2 + y2, 251 (b) F(x, y, z) = (z, x-z, y), S is the triangle with vertices (1,0,0), (0, 1,0), and (0,0,1), oriented downward (c) F-(y. -x,z), S is the upward helicoid parametrized by r(u, v) = (UCOS v, usin v,V), osus 2, OSVS (Hint: Tu x Ty = (sin v, -cos v, u).)...
Find the exact area of the surface obtained by rotating the
curve about the x-axis.
y = sin( mx), osxs9
Question 8 (1 mark) Attempt 1 S is the surface y2 36(2+22 A suitable parametric representation of the surface S is: yE(0,6] obtained by rotating the function y 60 about the y-axis for yE[0,6]. _ A (s,e) scos0i+6s2j+ssin0k, 0<s<1, 0<e<2r B T(s,0)scosei+ssin@j+6s2k, 0s1, 0e<2m C Ts, scosei+ssin0j+6sk, 0s1, 0<e<2n (s,0) 6s22+scosej+ssin0k, 0<s<1, 0<0<2 O D OE T(s,) 6st+scosGjssin6k, 0s1, 0<e<2T F T(s,e) scos01+6sj+ssin0k, 0<s<1, 0<0< 2T None of these OG
Question 8 (1 mark) Attempt 1 S is the surface...
Question 8 (1 mark) Attempt 4 ye[0,9 S is the surface y 9(r2+22), ye[0,9] A suitable parametric representation of the surface S is 92 aboute the y-axis for obtained by rotating the functiony= r(s,0) scosi+9sj+ssin@k, 0<<s<1, 0<0<2r O A r(s,0)=scos0i+9s2j+ssin0k, 0<s<1, 0<0<2« B T(s,0)=scos0i+ssinej+9s2k, 0<s<1, 0<0<2« r(s,0)=scosi+ssin@j+9sk, 0<s<1, 0<0<2« D r(s,0)=9si+scos@j+ssin0k, 0 <s<1, 0<0<2T E T(s,0)=9s2i+scosej+ssin0k, 0<s<1, 0<0<2 F G None of these.
Question 8 (1 mark) Attempt 4 ye[0,9 S is the surface y 9(r2+22), ye[0,9] A suitable parametric...
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