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Question 1 Find a parametric representation of the part of the cylinder x? +2 - 9that...
2. Evaluate the surface integral [[Fids. (a) F(x, y, z) - xi + yj + 2zk,...
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).)...
9. Find the parametric representation of each surface. a. The part of the hyperboloid 2 -xy-1 that lies above the rectangle [-2,2]*[-5,5]. b. The part of the sphere x2 +y2 +22-16 in the first oct...
9. Find the parametric representation of each surface. a. The part of the hyperboloid 2 -xy-1 that lies above the rectangle [-2,2]*[-5,5]. b. The part of the sphere x2 +y2 +22-16 in the first octant that lies above the cone
9. Find the parametric representation of each surface. a. The part of the hyperboloid 2 -xy-1 that lies above the rectangle [-2,2]*[-5,5]. b. The part of the sphere x2 +y2 +22-16 in the first octant that lies above the cone
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...
1 a) Find the domain of r(t) = (2-Int ) and the value of r(to) for...
1 a) Find the domain of r(t) = (2-Int ) and the value of r(to) for to = 1. b) Sketch (neatly) the line segment represented by the vector equation: r=2 i+tj; -1 <t<l. c) Show that the graph of r(t) = tsin(t) i + tcos(t) j + t?k, t> 0 lies on the paraboloid: z= x2 + y². 2. a) Find r'(t) where r(t) = eti - 2cos(31) j b) Find the parametric equation of the line tangent to...
PLEASE ANSWER EACH QUESTION FOR UPVOTE! THANK U! 1.) Which of the following parametric equations are equivalent to the p...
PLEASE ANSWER EACH QUESTION FOR UPVOTE! THANK U!
1.) Which of the following parametric equations are equivalent to
the polar equation r(theta) = cos(theta) cot(theta)?
A) x = sin^2(theta) and y = sin^2(theta) cot(theta)
B) x = cos^2(theta) and y = cos^2(theta) cot(theta)
C) x = cos^2(theta) cot(theta) and y = cos^2(theta)
D) x = cos(theta) cot(theta) and y = cos(theta)
2.)Which describes the parametric equations x = 2t and y = 4sin
t?
A) y = x^2 + 2...
Prove the arithmetic properties of the Cross Product 1. 2. a. Line L1 is parallel to the vector u...
please answer question 4-7
Prove the arithmetic properties of the Cross Product 1. 2. a. Line L1 is parallel to the vector u Si+j, line L2 is parallel to the vector u-3i +4j and both lines pass through point P(-1,-2). Determine the parametric equations for line L1 and Lz b. Given line L:x(t)-2t+8,y(t)-10-3t. Does L and Ls has common 3. a. Find the equation of the plane A that pass through point P(3,-2,0) with b. Given A2 be the plane...
All of 10 questions, please. 1. Find and classify all the critical points of the function. f(x,y) - x2(y - 2) - y2 » 2. Evaluate the integral. 3. Determine the volume of the solid that is inside the...
All of 10 questions, please.
1. Find and classify all the critical points of the function. f(x,y) - x2(y - 2) - y2 » 2. Evaluate the integral. 3. Determine the volume of the solid that is inside the cylinder x2 + y2- 16 below z-2x2 + 2y2 and above the xy - plane. 4. Determine the surface area of the portion of 2x + 3y + 6z - 9 that is in the 1st octant. » 5. Evaluate JSxz...
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).)...
9. Find the parametric representation of each surface. a. The part of the hyperboloid 2 -xy-1 that lies above the rectangle [-2,2]*[-5,5]. b. The part of the sphere x2 +y2 +22-16 in the first octant that lies above the cone
9. Find the parametric representation of each surface. a. The part of the hyperboloid 2 -xy-1 that lies above the rectangle [-2,2]*[-5,5]. b. The part of the sphere x2 +y2 +22-16 in the first octant that lies above the cone
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...
1 a) Find the domain of r(t) = (2-Int ) and the value of r(to) for to = 1. b) Sketch (neatly) the line segment represented by the vector equation: r=2 i+tj; -1 <t<l. c) Show that the graph of r(t) = tsin(t) i + tcos(t) j + t?k, t> 0 lies on the paraboloid: z= x2 + y². 2. a) Find r'(t) where r(t) = eti - 2cos(31) j b) Find the parametric equation of the line tangent to...
PLEASE ANSWER EACH QUESTION FOR UPVOTE! THANK U!
1.) Which of the following parametric equations are equivalent to
the polar equation r(theta) = cos(theta) cot(theta)?
A) x = sin^2(theta) and y = sin^2(theta) cot(theta)
B) x = cos^2(theta) and y = cos^2(theta) cot(theta)
C) x = cos^2(theta) cot(theta) and y = cos^2(theta)
D) x = cos(theta) cot(theta) and y = cos(theta)
2.)Which describes the parametric equations x = 2t and y = 4sin
t?
A) y = x^2 + 2...
please answer question 4-7
Prove the arithmetic properties of the Cross Product 1. 2. a. Line L1 is parallel to the vector u Si+j, line L2 is parallel to the vector u-3i +4j and both lines pass through point P(-1,-2). Determine the parametric equations for line L1 and Lz b. Given line L:x(t)-2t+8,y(t)-10-3t. Does L and Ls has common 3. a. Find the equation of the plane A that pass through point P(3,-2,0) with b. Given A2 be the plane...
All of 10 questions, please.
1. Find and classify all the critical points of the function. f(x,y) - x2(y - 2) - y2 » 2. Evaluate the integral. 3. Determine the volume of the solid that is inside the cylinder x2 + y2- 16 below z-2x2 + 2y2 and above the xy - plane. 4. Determine the surface area of the portion of 2x + 3y + 6z - 9 that is in the 1st octant. » 5. Evaluate JSxz...
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