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If you were to figure out the tangent plane to the curve: z = cos(xy) at...
(b) Let C be the closed curve formed by intersecting the cylinder x2 +y= 1 with the plane x z= 2. Let the tangent to th...
(b) Let C be the closed curve formed by intersecting the cylinder x2 +y= 1 with the plane x z= 2. Let the tangent to the curve from above. point in the anti-clockwise direction when viewed Calculate the line integral (e (e sin y+ 4) dy+(e(cos z+ sin z)+ay) dz. cos x2yz) dx +
(b) Let C be the closed curve formed by intersecting the cylinder x2 +y= 1 with the plane x z= 2. Let the tangent to the...
Consider z-f(x,y)-1-xy cos(xy) at (2,-1/2) variations in x and y respectively. and let ΔΧ and ây ...
Consider z-f(x,y)-1-xy cos(xy) at (2,-1/2) variations in x and y respectively. and let ΔΧ and ây represent small a) (i) Compute ΔΖ, given that ΔΧ_ 0.028 and Δy_-0.039. 1 1 6DP Az 5DP ii) Write out an expression for dz in terms of x,y and d, dy. dz= 2 (iii) Compute dz assuming dr_Δι and dy_ây dz- 5DP b) Use the equation of the tangent plane to z at (2,-1/2) to approximate Approximate value = 1 5DP
Consider z-f(x,y)-1-xy cos(xy)...
In this exercise you will figure out the equipotential point/points(s)/line/surface in the xy plane where V...
In this exercise you will figure out the equipotential point/points(s)/line/surface in the xy plane where V = 0 for two point charges of charge q and -2q found respectively at (x,y,z) = (-1,0,0) and (x,y,z) = (1,0,0), and draw the result on Fig. ??. (a) Given that V is a scalar, equipotentials generally form surfaces in three di- mensions. This contrasts with the electric field, where we found only one position where it was zero for a pair of point...
(4) Consider the surface z = x2+4y2+1. Suppose you are walking on this surface directly above a curve C in the xy-plane, where the parameterized curve is given by C (t)cost, y(t) sin t. Find the valu...
(4) Consider the surface z = x2+4y2+1. Suppose you are walking on this surface directly above a curve C in the xy-plane, where the parameterized curve is given by C (t)cost, y(t) sin t. Find the values of t for which you are walking uphil increasing z (Assume you are walking above the curve C in the direction of positive orientation The direction of positive orientation for the plane curve C is indicated by its tangent vectors.)
(4) Consider the...
Consider the following function 6 f(x, y,z)=z - x? cos(my) + xy? (i) Find the gradient...
Consider the following function 6 f(x, y,z)=z - x? cos(my) + xy? (i) Find the gradient of the function f(x, y, z) at the point P,(2,-1,-7). (ii) Find the directional derivative of f(x, y, z) at P,(2,-1,-7) along the direction of the vector ū = 2î+j+2k. (iii) Find the equation of the tangent plane to the surface given below at the point P,(2,-1, -7). 6 :- xcos(ty) + = 0 xy
e.) What is the equation of the tangent plane to the function z = x2 +...
e.) What is the equation of the tangent plane to the function z = x2 + 4y2 at the point with x = 2, y = -1? [8 points) f.) For the curve through space F(t) =< sin(3t), cos(3t), 2t>, what is the unit tangent vector at t = 7/2? [8 points] g.) Starting from t= 0, reparameterize the curve r(t) = (1 - 2t) î +(-4+ 2t)ſ+(-3 – t)k in terms of arclength. [8 points]
5e= 2y at the point (4, 8, 5) |Find the tangent plane to the equation z...
5e= 2y at the point (4, 8, 5) |Find the tangent plane to the equation z Preview xy at the point (6,8,10), and use it to approximate f(6.15, 8.19) 12 Find the linear approximation to the equation f(x, y) = 5, Preview f(6.15, 8.19) Make sure your answer is accurate to at least three decimal places, or give an exact answer
5e= 2y at the point (4, 8, 5) |Find the tangent plane to the equation z Preview
xy at...
Question 1 < Find the tangent plane to the equation z = 3.12 2y2 + 3y...
Question 1 < Find the tangent plane to the equation z = 3.12 2y2 + 3y at the point (-4, -3, - 75) 2 Question 2 Find the tangent plane to the equation z = 5ex°-by at the point (12, 24, 5) Question 3 < > Find the tangent plane to the equation z = 5y cos(3x – 2y) at the point (2,3,15) z = Question 4 at the point (4,2,8), and use it to Find the linear approximation to...
Consider the surface z = f(x, y) = sin(x) + cos(y) and the curve C in...
Consider the surface z = f(x, y) = sin(x) + cos(y) and the curve C in the xy plane defined parametrically as x(t) = 2cos(t), y(t) = sin(t) a. Find z'(t). Imagine you are walking directly above the curve C in the direction of increasing t. Find the values of t for which you are walking uphill. Hint:Graph z'(t). Graph f(x, y) for -7 < x < 7 and -7 < y < 7. (You will have to find software...
([8]) Find the point on the surface z = x2 + 2y2 where the tangent plane...
([8]) Find the point on the surface z = x2 + 2y2 where the tangent plane is orthogonal to the line connecting the points (3,0,1) and (1,4,0). Useful formula: The curvature of the plane curve y = f(x) is given by k(x) = \f"|(1 + f/2)-3/2, ([9]) Use spherical coordinates to find the volume of the solid situated below x2 + y2 + 2 = 1 and above z= V x2 + y2 and lying in the first octant.
(b) Let C be the closed curve formed by intersecting the cylinder x2 +y= 1 with the plane x z= 2. Let the tangent to the curve from above. point in the anti-clockwise direction when viewed Calculate the line integral (e (e sin y+ 4) dy+(e(cos z+ sin z)+ay) dz. cos x2yz) dx +
(b) Let C be the closed curve formed by intersecting the cylinder x2 +y= 1 with the plane x z= 2. Let the tangent to the...
Consider z-f(x,y)-1-xy cos(xy) at (2,-1/2) variations in x and y respectively. and let ΔΧ and ây represent small a) (i) Compute ΔΖ, given that ΔΧ_ 0.028 and Δy_-0.039. 1 1 6DP Az 5DP ii) Write out an expression for dz in terms of x,y and d, dy. dz= 2 (iii) Compute dz assuming dr_Δι and dy_ây dz- 5DP b) Use the equation of the tangent plane to z at (2,-1/2) to approximate Approximate value = 1 5DP
Consider z-f(x,y)-1-xy cos(xy)...
(4) Consider the surface z = x2+4y2+1. Suppose you are walking on this surface directly above a curve C in the xy-plane, where the parameterized curve is given by C (t)cost, y(t) sin t. Find the values of t for which you are walking uphil increasing z (Assume you are walking above the curve C in the direction of positive orientation The direction of positive orientation for the plane curve C is indicated by its tangent vectors.)
(4) Consider the...
Consider the following function 6 f(x, y,z)=z - x? cos(my) + xy? (i) Find the gradient of the function f(x, y, z) at the point P,(2,-1,-7). (ii) Find the directional derivative of f(x, y, z) at P,(2,-1,-7) along the direction of the vector ū = 2î+j+2k. (iii) Find the equation of the tangent plane to the surface given below at the point P,(2,-1, -7). 6 :- xcos(ty) + = 0 xy
e.) What is the equation of the tangent plane to the function z = x2 + 4y2 at the point with x = 2, y = -1? [8 points) f.) For the curve through space F(t) =< sin(3t), cos(3t), 2t>, what is the unit tangent vector at t = 7/2? [8 points] g.) Starting from t= 0, reparameterize the curve r(t) = (1 - 2t) î +(-4+ 2t)ſ+(-3 – t)k in terms of arclength. [8 points]
5e= 2y at the point (4, 8, 5) |Find the tangent plane to the equation z Preview xy at the point (6,8,10), and use it to approximate f(6.15, 8.19) 12 Find the linear approximation to the equation f(x, y) = 5, Preview f(6.15, 8.19) Make sure your answer is accurate to at least three decimal places, or give an exact answer
5e= 2y at the point (4, 8, 5) |Find the tangent plane to the equation z Preview
xy at...
Question 1 < Find the tangent plane to the equation z = 3.12 2y2 + 3y at the point (-4, -3, - 75) 2 Question 2 Find the tangent plane to the equation z = 5ex°-by at the point (12, 24, 5) Question 3 < > Find the tangent plane to the equation z = 5y cos(3x – 2y) at the point (2,3,15) z = Question 4 at the point (4,2,8), and use it to Find the linear approximation to...
Consider the surface z = f(x, y) = sin(x) + cos(y) and the curve C in the xy plane defined parametrically as x(t) = 2cos(t), y(t) = sin(t) a. Find z'(t). Imagine you are walking directly above the curve C in the direction of increasing t. Find the values of t for which you are walking uphill. Hint:Graph z'(t). Graph f(x, y) for -7 < x < 7 and -7 < y < 7. (You will have to find software...
([8]) Find the point on the surface z = x2 + 2y2 where the tangent plane is orthogonal to the line connecting the points (3,0,1) and (1,4,0). Useful formula: The curvature of the plane curve y = f(x) is given by k(x) = \f"|(1 + f/2)-3/2, ([9]) Use spherical coordinates to find the volume of the solid situated below x2 + y2 + 2 = 1 and above z= V x2 + y2 and lying in the first octant.
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