Let f(r, y, 2) = 2ry + 2. Evaluate f(1, y, 2) dz where C is the portion of the helix r(t) = cos ti+ sin tj–2t k; 0

Q: · Find fF · dĩ for F = -yi – 4x j+4zk if C is the helix æ = cos t, y = sin t, z = t, for 0 < t < 47

A: Given F→=-yi→-4xj→+4zk→

Q: a) Evaluate Vx² + y² dydx. 1 J-Vi b) Evaluate the line integral | cos x cos y da + (1 – sin æ sin y)…

A:

Q: Find the equation for the rectifying plane at the point that corresponds to that value of t. r(t) =…

A:

Q: 6) Find the equation of the osculating plane of the helix x = sin 3t, y = 2t, z = cos 3t at the…

A:

Q: Determine the direction at t= pie/2 where R is 2sin t i + 2 cos t j + 2t k

A:

Q: Show that the function f(x, y) x4 + y? has no limit as (x, y) approaches (0,0).

A: Note: Since we can solve at most one problem at a time, we have solved the first one. Kindly…

Q: Calculate F.dr, where C is the curve given by ti + 123+ tk, with t = [0, 1] and F(x, y, z) = 4xei +…

A:

Q: Evaluate I = f (z, x, y). dr and C is the helix of r(t) = (cost, sin t, 3t) sketch the curve C.

A: Given,               I=∫Cz, x, y·dr, and C is the helix of r(t)=cost, sint, 3t.

Q: COS 1,sin 2t) and R(0) = (1,0.–1). Let R be a vector function such that T(t) = (cos 2t, 2/2, Find An…

A: Given : T→=32cos2t , 12 , 32sin2t, R→0=1 , 0 , -1. To Find: The equation of the osculating plane,…

Q: Find the Jacobian for the change of variables defined by x = r cos θ and y = r sin θ.

A: To calculate the Jacobian for the change of variables, we need to calculate the following…

Q: Let y be the hypocycloid R(t) = (8 cos³ t, 8 sin³ t), t = [0, 27], and C the portion of Y from the…

A:

Q: The vector function r(t) (5 – 2 sin t) i+ (3+2 cos t) j+ 2k traces out a circle in 3-space as t…

A:

Q: 2. Find thé moving trihedral of the curve C traced by the vector-valued function R(t) 4 cost i+4…

A:

Q: The helix F(t) = 4cos(t)i + 2 sin(t)j + 5tk is shown below. By setting the last component to zero…

A: Given that,Equation of a helix isr→(t)=4cos(t)i^+2sin(t)j^+5tk^The projection of this curve into the…

Q: F(t) = %3D a. elliptical helix |F(t) = b. conical helix %3D ]F(t) = c. line d. circular helix…

A: We will use standard parametric form of these curve to match   For circle x = a cos(t) y = a sin(t)…

Q: Use Green's Theorem to evaluate fa F. dr where F(x, y) = (y cos x, x² + 2y sin x) and C is the…

A:

Q: Let r(t) = (et, et sin t, et cos t).  Find the equation of the plane that is normal to the curve at…

A:

Q: af ar fe Consider f(1, y, z) = r² + y²z² and I=r sin 0, y =r cos 0, z = Or³. Find and

A: The function fx,y,z=x2+y2z2 and the polar transformation coordinates are x=rsinθ, x=rcosθ and z=θr3.…

Q: A glider is soaring upward along the helix r(t) = (cos t)i + (sin t)j + tk. How long is the glider’s…

A: Given: The path of glider as r→t=cost i^+sint j^+t k^, To find: The length of the glider's path from…

Q: The parametric curve 7(t) = t2 i + (3 – t) j + et k as: 2t – 1+ e = 0 - = ť², y = 3 – t, z = et t? +…

A:

Q: Evaluate aned on c indicatid curve 2. 2. y+ Y( sm3x +ca 32,22 3t ,4=t,0zt2|

A: