How many dependent scalar variables does the function r(t) = ⟨ƒ(t), g(t), h(t)⟩ have?

Q: Find the gradient of the function z = cos(x2 + y2), at the given point (3, −4)

A: Given=z=cos x2+y2 at point x,y=3,-4Gradient∇x,y=fxx,yi+fyx,yjwhere fx,y=z=cos x2+y2

Q: 2. Find the derivative of the function at PO in the direction of u. f(x,y)=6x-7y, P0(-7,-2), u=4i-3j

A: We have to find derivative

Q: Find the gradient of the function at the given point.

A:

Q: 1. Explain why / f'(t) dt = f(b) – f (a). ||

A: Refer to image below.

Q: The function f(x, y, z) = x² – y² = z² increases in the direction at the point (1, 1, 1).

A: We need to find if the statement is true or false.

Q: _12. What is the maximum directional derivative Daf of the function f(x,y,z) = x – y² + z² at the…

A: Let's find.

Q: Find the gradient of the function at the given point. f(x, y) = 2x + 4y2 + 4, (1, 2) Vf(1, 2) =

A:

Q: the linearization of (fi,f2) = (x²y+ 3xy², 3x³ + 2xy) at (1,0) to approximate the value at…

A:

Q: Find the gradient of the function at the given point. f(x, y) = 2x + 5y² +6, (3, 1) Vf(3, 1) =

A:

Q: Find the gradient of the function at the given point. f(x, y) = 2x + 5y2 +6, (3, 1) Vf(3, 1) = 2i+…

A:

Q: Find the gradient of the function at the given point. f(x, y) = 3x + 5y2 + 8, (2, 1) Vf(2, 1) =

A: We have given function  fx,y=3x+5y2+8 fx=∂fx,y∂x fx=3∂x∂x+5∂y2∂x+∂8∂x fx=3+0+0 fx=3  .........(i)…

Q: Assume that f(x) is a differentiable and invertible function so that f(3) = 4 and f'(3) = .…

A:

Q: Find the gradient of the function at the given point. f(x, y) = 4x + 2y2 + 10, (2, 3) Vf(2, 3) =

A:

Q: | f(t) dt = x*e* e + a

A: This question is based on integration.

Q: Find the direction at which the function f(x, y, z) = x In(e - cz) increases fastest at (-3, C O (0,…

A: To Find: The direction at which the function  fx,y,z=x ln(ey -xz) increases fastest at ( -3, 0 ,0)…

Q: Find the directional derivative of f(x, y) = In(e"- 3y) at the point (0,0) in the direction of 3i +…

A: We are asked to find directional derivatives of function.

Q: Find the linearization of the function z = x/j at the point (3, 64). L(x,y)

A: According to the Bartleby guideline only one question can be solved at one time, post the remaining…

Q: Find a point zo where the function f (z) = (z – 12 – 12i) (z – 12 – 12i) is differentiable. What is…

A: Given f(z) = (z-12-12i)(z -12 -12i)¯

Q: Solve for the gradient of the given function. f(x, y) = e" sin y + e cos x

A:

Q: Find the derivative of the given function at P. (3, 3, 3) in the direction of u = 3i + 4j f (x, y,…

A:

Q: Find the direction at which the function f(x, y, z) increases fastest at (2, 0, 0) = x In(e' – xz)…

A:

Q: 3 ) Express f(t) in terms of the unit step function u(t).

A:

Q: Find the gradient of the function at the given point. f(x, y) = 2x + 4y2 + 8,    (2, 1) ∇f(2, 1) =

A: We have to find the gradient of the function  f(x, y) = 2x+4y2+8  at the point (2, 1).

Q: For the function f(x, y) = (cos x)ey +v 1 + x + y. %3D Show the process of using the linearization…

A:

Q: Find the derivative of the function. g(u) = (8+ u²)*(1 – 5u²)8 %3D = (n), 6

A: Now we will differentiate g with respect to  u . And we will  derivative the function using chain…

Q: 1. Find the Gradient of the following F = x*e" - y': b. F, = 4x - 3y + 5=? а.

A:

Q: |dx + N(x,y)dy = 0 x² + y,

A:

Q: Find the directional derivatives of f(x,y,z) = x² y³ – y³z³ + x* in the direction of r = 2i– k, and…

A:

Q: What does it mean for the differentiability of a function if only one of the Cauchy-Reimann…

A:

Q: Find of the function f(x,y) = sin(x²y³). əx3

A: The product rule of differentiation : (PQ)'=PQ'+QP' sinx'=cosxcosx'=-sinxxn'=nxn-1 Use the given…

Q: Find the gradient of the function at the given point. f(x, y) = 4x + 3y² + 8, (2, 1) Vf(2, 1) =

A:

Q: 1. Find the Gradient of the following a. F, = x'e" - y': b. F, = 4x' - 3y +5=?

A: Solution is given as below:

Q: Find the gradient of the function at the given point. f(x, y) = 4x + 3y² + 8, (2, 1) Vf(2, 1) = 4i +…

A:

Q: Find the derivative of the function at Po in the direction of u. f(x, y) = In(-10x - 7y), P o(-4,…

A:

Q: Let Dx be the linear transformation from C'[a, b] into Cla, b]. Find the preimage of the function.…

A:

Q: Let Dx be the linear transformation from C'[a, b] into C[a, b]. Find the preimage of the function.…

A: Solution: Consider the given linear transformation : Dxf = 2x + 3 Since D is the linear…

Q: Find the linearization L(æ) of the function at a. f(z) = V7, a = -8 L(x)

A: We can find the linearization as below.

Q: Let Dx be the linear transformation from C'[a, b] into C[a, b]. Find the preimage of the function.…

A: We have to solve above question and find preimage function

Q: Apply the first part of the fundamental theorem to determine the value of F'(x) if: e) F (x) = S…

A:

Q: Find the directional derivative of f(x, y) = In(e" - 2y) at the point (0,0) %3D in the direction of…

A: take the partial derivative with respect to x put the point (0,0)

Q: Find the linearization of the function at the given point. f (x, y) = e sin y, 0, 7).

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Find the linearization of the function f(x,y) = y + sin (x/y) at the point (pi,3)

A:

Q: Find the linearization L(x) of the function at a. f(x) = sin(x), a = %3D L(x) = %3D

A:

Q: Integrate the function f(x, y) = x – y over the triangle T with vertices (0,0), (1,0), and (1, 2).

A: Evaluate : ∫∫T(x-y)dA        ......(1) ∫∫Tx-ydydx T is the region enclosed by the triangle. Region…

Q: Find the linearization of the function f (x, y, z) = -6xy+ 9yz + 8zx at the point (1, 1, 1)

A:

Q: Find the gradient of the function at the given point. f(x, y) = 4x + 3y2 + 1, (1, 4)

A: To find the gradient of the function at the given point.

Q: Suppose w is a function of x, y, and z, which are each functions of t. Explain how to find dw/dt.

A: Given data:"w" is a function of (x,y,z). Therefore, w(x,y,z). And the function x, y and z are the…

Q: 4. What is the direction in which the function f(x, y) = yx² -- decreases most rapidly at the point…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Find the gradient of the function at the given point. f(x, y) = 4x + 2y² + 4, (1, 2) Vf(1, 2) =

A:

Q: Find the gradient of the function at the given point. f(x, y) = 4x + 3y2 + 1, (1, 4) Vf(1, 4) =

A:

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.