Find the domain of the vector function 7(t) = (v4 – t², e-3t, ln(t + 1)

Q: Find the derivative of the vector function r(t) = ta x (b+tc), where а 3 (—3, —4, — 2), b — (—2, —5,…

A: Topic:- vector and it's derivatives

Q: Find the directional derivative of the function f: R2→R,  f (x, y)= xy2 + x2y in the direction of…

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Q: find the vector function r(t) given r'(t) and the initial condition

A: Solution: The objective is to find the vector function r(t)

Q: Match the vector field with its graph. F(x, y) = xi + 3yj + +x ' ||||||||||| 畫 至 X

A: Solution is given below:

Q: State whether the following derivatives of vector-valued functionsr1(t) and r2(t) are scalars or…

A: To find:  whether the derivatives of vector-valued functions r1(t) and r2(t) are scalars or…

Q: Find the gradient vector field of f(x, y, z) = 9x² + 8y* + 6z3

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Q: Find a potential function for the vector field F(x, y) = (14xy + 7y- 8, 7z + 7z). f(x, y) =

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Q: Find the derivative of the vector function r(t) = In(18 – 12) i+ v5+tj- 9e“ k r' (t) = (

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Q: Express the following as a vector valued function 7 (t). 1. The line L defined by y+3=3x and z+1 =0…

A: We will express the line L defined by y+3=3x and z+1=0 hyperbola -x2-2x+2y2+4y=-2 as a vector valued…

Q: Match the vector field with its graph. F(x, y) = yi -6+

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Q: Find the gradient vector field of f(x,y) = x2 + y2 and sketch it.

A: Solution

Q: Match the vector field with its graph. F(x, y) = xi + 3yj 5 y -6+

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Q: Consider the vector-valued function [f(x, y) xt – xy² [g(x, y) 2 Vx + y³x² [f(x, y) Which of the…

A: Find the Jacobian of the given matrix

Q: 2. Show that the given vector functions are linearly dependent on (-0,00). e' x(t) = x, (t) = 4e 2e2…

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Q: Find the gradient vector field of f(x, y, z) = e3r + 8y+6z

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Q: -2 -1

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Q: Find the gradient vector field of f(x, y, z) 5x+ 2y+8z

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Q: 10. Draw the graph of the vector-valued functions (a) for the plane curve, r(t) = 2cost³i + 3sint³j,…

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Q: Find the derivative of the vector function r(t) = In(13 – t²)i+ y13+tj– 9e 3 k r'(t) = {

A: The given vector function is                                   r(t)=ln13-t2i+13+tj-9e-3tk

Q: (b) Identify the unit vector u pointing in the direction of maximum increase of the function f(x, y)…

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Q: Find the derivative of the vector function r(t) = ta x (b+tc), where (5,-4, 1), b = {(-4, –3,1), and…

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Q: Find a potential function of the vector field. F(x,y) = (3x²y + 1, x³+2y)

A: we have to find potential function.

Q: Find the domain of the vector function T (ty= Vt + 7 Domain: {t <t< }

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Q: Find the derivative of the vector function r(t) = In(13 – ) i+ v3 +ij+ le- k r' (t) = (

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Q: Match the vector field with its graph. F(x, y) = xi + 3yj -st

A: Plot the given vector Fx,y=xi+3yj.

Q: Match the vector field with its graph. F(x, y) %3D хі + Зуј -67

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Q: Find the domain of the vector-valued function. (E r(t) = V 25 - t2i + t²j - 2tk tj- 2tk

A: Solution by using definition :

Q: 1. Consider f(x, y) = 2x² – y² + 3x – y and U is any unit vector in R2. Find the maximum value of…

A: To find maximum value of DUf at x=1, y= -2 we shall use the given definition

Q: Match the vector field with its graph. F(x, y) = xi + 3yj 5

A: We can solve this using by draw a graph

Q: f(x,y) = 2x3+4y3-3x2-120x-192y+5 Is f(x,y) a curve, vector field, or surface?

A: To check whether it is a curve, vector or surface. f(x,y) = 2x3+4y3-3x2-120x-192y+5

Q: Is the vector valued function continuous at t=3? Defend your answer. I² -9 t- 3 V3t – 1, In(4 – t),…

A: Topic = Continuity

Q: Why is r(t) = ⟨ƒ(t), g(t), h(t)⟩ called a vector-valued function?

A: Given r(t) = ⟨ƒ(t), g(t), h(t)⟩. We need to give reason why r(t) is called vector-valued function.

Q: (b) Identify the unit vector ū pointing in the direction of maximum increase of the function f(x, y)…

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Q: Match the vector field with its graph. F(x, y) = xi + 3yj 1信 -6 5 to -5+

A: We have to take point (x,y) and then draw vector field

Q: Find the gradient vector field ∇f of f(x, y) = x2 − 4y.

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Q: Find the derivative, r'(t), of the vector function. r(t) = (e-t, 6t – t3, In(t))

A: Solution-  Given vector function  r(t) = (e-t, 6t-t3, ln (t)) We have to differentiate these…

Q: The vector-function gives a particle velocity as function of time: T(t) =, and the particle position…

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Q: (b) Identify the unit vector u pointing in the direction of maximum increase of the function f(x, y)…

A: Find your answer below

Q: A. Express the following as a vector valued function 7 (t). 1. The line L defined by y+3=3x and z+1…

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Q: Find the derivative, r'(t), of the vector function. r(t) = (e-t, 4t - t, In(t) r'(t)

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Q: Find the gradient vector field of f(x, y, z) = e® 5x+2y+8z

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Q: Find a vector-valued function whose graph is the indicated surface: the part of the paraboloid z =…

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Q: Match the vector field with its graph. F(x, y) = xi + 3yj KE 、 ||十

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Q: Match the vector field with its graph. F(x, y) = xi + 3yj 5- 5 -5+ -5+

A: Given data÷

Q: Find the derivative of the vector function r(t) = ta x (b + tc), where a = (2,-2, 5), b (2,-5, 3),…

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Q: Find the domain of the vector-valued function r(t)=ln(t-1)i+Square root 4-tj

A: This vector valued function is a combination  of two functions: 1. Logarithmic function and 2.…

Q: Find the derivative of the vector function r(t) = In(5 – t²)i+/16 +tj+ 7e 8t k r'(t) = (

A: Given vector valued function is rt=ln5-t2i+16+tj+7e-8tk

Q: Find the gradient vector field of f(x, y, z) = e9z+6y+7z V

A:

Q: Find the derivative of the vector function ta x (b tc), where r(t) = (-1,1,-2) а %3 (-2,3, -1), ь 3…

A: Given vector function is,