3. [F. dR, where F(x, y, z) = (z, x, y) and C : R(t) = 2 cost î+ 3 sint ĵ + sin² tk, 0 ≤ t ≤ et, T is the unit tangent vector to C: R(t), 0 ≤ t ≤ 1, at [ F · dŘ, where F(R(t)) · Ï(t) = any t, and ||Ẩ' (t)|| = √√√2 et 2

Q: Consider the function 3..2 f(x, y) = cos(rxy) – a°y?. = cos(Txy) – x°y°. a) Find the equation of the…

A:

Q: For the function f(x, y) = x² 4xy + 4y² + 4x + 5y + 4, find a unit tangent vector to the level curve…

A:

Q: . Let n 2 3 be an odd number and f(a, y) = (x" + y")'/n. (a) Determine if f(x, y) is differentiable…

A: We will only use the basic knowledge of the differentiability of functions of two variables to…

Q: For the given position vectors r(t) compute the unit tangent vector T(t) for the given value of t.…

A:

Q: Find the equation of the tangent plane to z = x² + 5y³ at (2, 1, 9).

A:

Q: Consider w = F(x,y,z) = x2 + yz3 Find the equation of the tangent when x= 3, y = 2, z = 1.  At…

A: The given surface is Fx,y,z=x2+yz3. (1) The given point is x=3,y=2, z=1. We know that the equation…

Q: The tangent line to the curve r(t) =(t°,t“, t³ ) at the point (1, 1, 1) intersects the æy-plane at a…

A:

Q: 1. Let R and b be positive constants. The vector function r(t) = (R cost, R sint, bt) traces out a…

A:

Q: O a) 10 b) 29 Oc) 17 d) 13 Oe) 1

A: Topic:- calculus

Q: 2. Let 3 – 4ry? 12 + y? if (x, y) # (0,0) f(x, y) = if (x, y) = (0,0) %3D (a) Is f differentiable at…

A:

Q: For f(x,y, z) = x² – (1 – y)² + z?. Find directional derivative of f at P(1,1,1) in the direction of…

A: The directional derivative of a function f  in the direction of the vector u is given by…

Q: 4. Let f(x, y) = sin(x²y) + vx + e+y. Find the equation of the tangent plane to the surface z f(x,…

A:

Q: 2. Let C be the graph of R(t) = (t sint, t³). a. Using the definition, show that Ŕ(t) is continuous…

A:

Q: Let f(x,y)= e, Compute the cartesian equation of the tangent plane r,y) at the point (2.2).

A: The equation of tangent plane

Q: t f(x, y) = x² cos(xy). ) Determine f(x, y). Determine fy(x, y). Determine Vƒ(1, π).

A: Topic:- application of derivatives     Note:- as per our guideline if more than three subparts…

Q: Next Consider the two vector-valued functions given by r(t) = (t+1, cos 1+t w(+) = (*, sin() *) . a.…

A: (a) The two vector valued functions intersect if r(a) = w(b) for some t = a and s = b.…

Q: For the function f(x, y) = 2x² – 3xy + 8y² + 2x – 4y + 4, find a tangent vector to the level curve…

A:

Q: A particle moves in the xy plane so that at any time -2 ≤ t ≤ 2, x = 3 sint and y = t - 4 cost + 1.…

A: A particle moves in the xy plane so that at any time ,  and .What is the vertical component of the…

Q: Let F(x,y,z) = (y,x²,zy) where C:R(t) = (cost,sin t , 3t) and t e [0,2]. Evaluate %3D %3D •dR

A: We have to find value of given Integral.

Q: 2. Let C be the graph of R(t) = (t sint, t³). a. Using the definition, show that Ŕ(t) is continuous…

A: