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(1 point) Let F = (5+* +1) i + sin(t)j +e5tk Find F'(t), F"(t) and F"(t)...
Questions 1 and 2 1. Find the gradient of f(I, y) = sin(Zy+5). 2. Let f(x, y, z) - ryz + x) (a) Find the gradient of f. (b) Find an equation of the tangent plane to the level surface ryz + 2 = 5 at the point (2,1,1).
(I point) Let F=21+(z + y) j + (z _ y + z) k. (1+4t). y = 4 + 2t, z = _ (1+t). Let the line l be x =- (a) Find a point P-(zo, 30, zo) where F is parallel to 1. Find a point Q (which F and I are perpendicular. Q= and l are perpendicular Give an equation for the set of all points at which F and l are perpendicular. equation: (I point) Let F=21+(z...
1. Consider the curve i(t) = (t sin(t) + cos(t))i + (sin(t) – t)j + tk. (a) Find the length of the curve for 0 <t<5. (b) Is the curve parameterized by arc length? Justify your answer. (C) If possible, find the arc length function, s.
6. Let the function r(t) = t cos((1 – 2a)t)i + t sin((1 – 2a)t)j + (2a – 1)tk over the interval [0, 41]. Find the value of a that gives the smallest arclength. Hint: There is a large amount of work in the middle of the problem that you can completely avoid. [10 marks]
Let f(n) = 5 sin(31) (I). Find the one-sided df) Laplace transform off) and g(t) = initial conditions are zero.
Calculus 4 Let f(x,y) = A)-i-j E) i+j 1. Find the gradient vector Vf (1, 1) at the point (x,y) = (1,1). B) - 1 - 1 D)-i-j 10. . Find the largest value of the directional derivative of the function f(x,y) = ry + 2ya at the point (3,y) = (1,2). A) 53 ' B) V58 C) V63 D) 74 E) 85 y + The function (,y) = 2 + y2 + A) (-3,5), saddle point C) (-1,3), maximum...
If C is the curve given by r(t) = (1 + 3 sin t)i + (1+2 sin2t) j + (1 + 5 sin3t) k, 0 ≤t≤π/2 and F is the radial vector field F(x, y, z) = xi + yj + zk, compute the work done by F on a particle moving along C.
(1)Calculate the scalar curl of the vector field. F(x, y) = sin(x)i + 6 cos(x)j (2) Let F(x, y, z) = (2exz, 3 sin(xy), x7y2z6). (a) Find the divergence of F. (b)Find the curl of F. -/3 points v MARSVECTORCALC6 4.4.017. My Notes Ask You Calculate the scalar curl of the vector field. F(x, y) = sin(x)i + 6 cos(x)j -/8 points v MARSVECTORCALC6 4.4.023. My Notes Ask You Let F(x, y, z) = (2x2, 3 sin(xy), x?y2z6). (a) Find...
Hi need help for these Questions: a. Given f = yi + xzk and g = xyz2, determine (∇ x f ) . ∇g at the point (1,0,3) b. Point A lies on the curve r(t) = 2 cos t i + 2 sin t j + t k for the range 0 ≤ t ≤ 2π . At point A, the tangent vector is T = - 21/2i + 21/2j + k. Determine the co-ordinates of point A and...
Let F(t) = (– 2+ + 2, – 5e 4, - sin(5t)) Find the unit tangent vector T (t) at the point t T (0) - 0. Round to 4 decimal places.