Show that this curve y represents the vector (1,0) as v = 1- +0- in the sense that, for an arbitrary smooth function f(r, y) on R2, af af +0- dy v(f) = 1

Q: True or False: Given a function of two variables f(x, y), the vector Vf(a, b) is perpendicular to…

A: It is false. The gradient vector ∇fa,b is not perpendicular to the graph z=fx, y at the point with…

Q: Determine the interval (s) on which the vector-valued function r(t)=ti+(sqrtt+1j)+(t^2+1)k…

A: The answer is given below:

Q: Let f(x,y,z) = x2 y−xy2+z3, P(1,1,2), u is the vector from P to Q(1, −2, −2). Determine the maximum…

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Q: Let f(x, y, z) = x²y - xy² + z³, P(1,1,2), u is the vector from P to Q(1, -2,-2). Determine the…

A: The given problem is to determine the maximum and minimum directional derivative of the given…

Q: Find r'(t), r(t), and r'(t) for the given value of to. Then sketch the space curve represented by…

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Q: Find the linearization of z = f(x,y) at P(-3, 2) when f(-3, 2) = 2 and f-(-3, 2) = 1, fy(-3, 2) =…

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Q: f f(x, y, z) = xy: on of vectorî - %3D

A:

Q: Compute ∇ƒ(-1, 2, 1), where ƒ(x, y, z) = xy/z.

A: Given,f(x,y,z)=xyz     As we know ∇f(x,y,z)=∂f∂x,∂f∂y,∂f∂z

Q: Suppose ƒ is differentiable at (9, 9), ∇ƒ(9, 9) = ⟨3, 1⟩, and w = (1, -1). Compute the directional…

A: Given that ∇ƒ(9, 9) = ⟨3, 1⟩. Note that w = (1, -1) is not a unit vector. Its unit vector along same…

Q: Let R be a differentiable vector-valued function such that R'(t) = (3t2, 2tvt2 + 1, 2t + 3) and R(1)…

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

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

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Q: 2. Consider the function f(x, y) = a) Find the directional derivative of f in the direction of the…

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Q: Suppose that f(I,2) =3 and that the directional derivative of fat point (1,2) in the direction of…

A: Thr given problem is to estimate the value of f(1.1,2.1) with given values f(1,2)=3 and directional…

Q: rative of the f he unit vecto p, then Ja + B|

A:

Q: #3. Consider the function xy2 if (x, y)# (0,0), f (x, y) = {x2+y2 if (x, y) = (0,0). Calculate the…

A: Given function is fx,y=xy2x2+y2if x,y≠0,00          if x,y=0,0 We have to calculate the directional…

Q: Where does the line with the vector equation [x,y,z] = [6, 7, -8] + t[-2, 4, 1] intersect the…

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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: 7. On a two-dimensional plane, sketch the vector |v>= such that it emanates from the coordinate…

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Vector Arithmetic

Vectors are those objects which have a magnitude along with the direction. In vector arithmetic, we will see how arithmetic operators like addition and multiplication are used on any two vectors. Arithmetic in basic means dealing with numbers. Here, magnitude means the length or the size of an object. The notation used is the arrow over the head of the vector indicating its direction.

Vector Calculus

Vector calculus is an important branch of mathematics and it relates two important branches of mathematics namely vector and calculus.