Show that F dr is independent of its path, given that F(r. y. :) = ( i+ tanrj+, + tan k. 1+:2 %3D Hence, find the potential function of F and then evaluate the work done by F moving an object along the smooth curve C, the line segment from (1,0,-1) to (0.0.0) then along the parabola 3 = y,r = 0 to (0.-1. 1). %3D %3D |

Q: Show that / F dr is independent of its path, given that F(r, y, :) = + tan-:) i+tan rj+ k. IHence,…

A: Here we will find out the required value and prove the required result.

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: b) Show that F - dr is independent of its path, given that y F(r, y, 2) = 1+. + tan-2) i+ tanrj+ k.…

A:

Q: Find torsion of the motion r(t) = . Leave your answer correct to two decimal places.

A:

Q: 3. Consider the following helix with vector equation 7 (t) = 2 cos (t) 7 (t) 7 + tỉ + 2 sin (a)…

A:

Q: A point moves along a right-circular helix C, which is the curve of the path 7 :R → R³ given by,…

A:

Q: [ sec2t dt + S sin?t dt + § n'-1dt

A:

Q: Find the equation of the tangent plane to z = e* + y + y° +1 at the point (0, 4, 70).

A:

Q: The functions f,6) = ¼cos² #/½ sin %3D are Neither linearly dependent or А. independent B. Linearly…

A:

Q: Consider the variable coefficient linear non-homogeneous ODE where and where u and are unknown…

A: The given problem is to find the values of u' and v' for the which the particular solution yp =…

Q: Example Let f(r,y, z) = ryz sin rz. Find Vfo at the point Po = (1, –2, 7) and compute the…

A: to find : (1) grad f. (2) directional derivative.

Q: Compute f cos(Tæ) dæ + 10xy dy, where y is a part of parabola y = 3x? from the point (0,0) to the…

A:

Q: Let 7(t) = (– 5t4 – 4, – 2e“, 2 sin(3t)) Find the unit tangent vector T (t) at the point t = 0 T (0)…

A:

Q: Find f. f(t) f"(t) = 2e + 3 sin t, f(0) = 0, f(π) = 0

A:

Q: Sketch the curve r(t)=f°i+tj and indicate the orientation. Find r'(t) and sketch r(1) & r°(1).

A: First we will plot the given parameters.

Q: 87; Let flxiy,2) =% Cos(Tx) + kon (s2). Then find the directional derivative of f the point…

A:

Q: Consider the tangent line to the curve r(t) = t2i −(1/(t + 1))j +(4 − t2)k at the point P(4, 1, 0).…

A: Given the tangent line to the curve r→t=t2i^−1t+1j^+4−t2k^  at the point P4,1,0. We have to…

Q: Let f(x, y) = 6x – 2ry and the point M(5, 9). Among all unit directions, there is a unit direction…

A:

Q: Compute the directional derivative of f(r. y) = = at the point (1, 1) in a irection normmal to the…

A:

Q: find dw/ar if w = (x + y + z)?, y = cos(r + s), at the point (r, s)3(1,-1) x = r - s, z = sin(r + s)

A: Given w=(x+y+z)2 x=r-s y=cos(r+s) z=sin(r+s) point (r, s)=(1, -1)   when we differentiate partially…

Q: Q3) For the following function: 1 U= zlog(x² + y²) 1. Determine whether it is harmonic (satisfy…

A:

Q: The position vector for a particle moving on a helix is c(t) = (3 cos(t), 2 sin(t), t²). (a) Find…

A: The position vector for particle moving on helix is ct=3cost, 2sint, t2. To find the speed of the…

Q: Determine un ju should be a plane curve. ion f (0) so that x = a cose, y = a sin0, z = f (0)

A:

Q: a) Compute the gradient of the function f(x, y, z) = e*y² . b)Compute the directional derivative Daf…

A:

Q: dy in terms of t: Differentiate parametrically to find dx 1 y = +2 t+1

A:

Q: Definition 3.27 Let P(x, y) be a point in R² and 0 be the radian measure of the angle formed by OP…

A:

Q: Given a function (r, y, 2) = 3x2 + In (3y2+ 1) + e cos 2. i. Find the directional derivative of o at…

A: Here we will find out the required value.

Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.