A7. Find Vf and Vf|| for the function f(x, y) = cosh(xy). At the point (1, 2) find the maximum rate of change of f. A8. A particle of mass m moves horizontally along the z-axis with velocity v=vi, subject to its weight P = -mgk where i and k are the standard orthonormal basis vectors in ther and direction. Show that the work of the weight P as the particle travels from x = 0 to z = L is zero.

Q: y6 16 (1). Consider z as a function of the variables x, y which is defined by z = ln(x®y) + and let…

A:

Q: The trajectories of two particles are given by the vector functions r1(t) = and r2(t) = Do the…

A: To find the point of intersection of the  vector functions r1(t) and r2(t) , equate r1(t) and r2(t)…

Q: . (Section 14.4) Let curve C be described by vector function(t) = (cost-1, sint, 3/2) on 0 ≤ t ≤ b.…

A: The curve C is defined by the function,on the interval,The length of the curve on the given interval…

Q: . Write an inline function that returns the value of the function f(t, x) = sin(Vx t) cos²(7x) and…

A: As per the question we have to construct an inline function that returns the value of the function :…

Q: Find r'(t), r(t), and r'(to) for the given value of to- r(t) = (e², e²t), to = 0 r'(t) = r(to) =…

A: rt=et,e2t,t0=0

Q: Find the maximum rate of change of f at the given point and the direction in which it occurs for…

A:

Q: 2.31 Let A and B be vector functions of position vector x with continuous first and second…

A: Let A and B be vector functions of position vector x with continuous first and second derivatives,…

Q: 5. Find the directional derivative of f(x, y) = y² + (x²/y), at the point (2, 1) in the direction of…

A:

Q: Suppose that over a certain region of space the electrical potential V is given by the following…

A: The given potential function is Vx,y,z=2x2-5xy+xyz. (a) To Find: Rate of change of the function at…

Q: 2. Consider the vector-valued function R(t) with Ả(1) = (1,2,−1) and R'(t): = (17/3/7-2) a) Find…

A: According to the guideline, only three subparts of the question can be answered. Please repost other…

Q: Find r'(t), r(t), and r'(to) for the given value of to. r(t) = (et, e24), to = 0 r'(t) = r(t) =…

A:

Q: Use the gradient to find a normal vector to the graph of the equation at the given point 7x²-y=5,…

A: In this question we have to find the Normal Vector using gradient.

Q: Determine if h(x, y) e* sinyī + e*cosyj is a gradient vector. If so, find f(xy) so that Vf=h(x, y).…

A:

Q: Find the maximum rate of change of f at the given point and the direction in which it occurs for…

A: Given: fx,y,z=3x+7yz 1,7,-1 To find: Maximum rate of change of f at the given point. The…

Q: R(t) = = {{In(3 In(3 – t), (0, -1, 4), 4t-8 4-t2⁹ 8), 3t² – 8 t#2 t = 2.

A:

Q: 3 - Find the Derivatives of the following Vectors, Where F(t)* = 2secti – 3j* + csctk and G(t)* =…

A:

Q: Repeat Exercise 27 for the forces KX = (2, – 3) and KY = (- 2, 3).

A: The given two force vectors are, KX→=2,-3KY→=-2,3 When we find the addition of two vectors, then the…

Q: 2 Consider the vector-valued function R(t) with Ả'(t) = (sec²(t – 1), √t' (a) Find R(t) given Ả(1) =…

A: a) Given: R'→t=sec2t-1, 2t, -2 and R→1=1, 0, -1 To find: R→t

Q: The directional derivative of the function f(x, y, z) = x³y4 – 3z2 at the point (1, 1,1) in the…

A: we have to find the directional derivative

Q: ar function = (1, 1, 2) i

A:

Q: Find a unit vector in the direction in which f(x, y) = 3r'y increases most rapidly at P(-1,1), and…

A: f(x, y)=3x7y9 P(-1, 1)

Q: t) = (et, e24), to = 0 لاخت لا rve represented by the vector-valued function, and sketch the vectors…

A:

Q: Q1. Find the vector function r(t) given that r(0)= i+2j. and r'(t)= (2et, 3t², 4 cost)

A: The given data is: r0=i+2jr't=2et, 3t2, 4cost Find the vector function rt