Let f(x+ y) = f(x).s) Vx, ye R.Prove that f is derivable on R iff it is derivable at one point of R.

Q: 4. Consider the function Check whether f is concave, convex or neither. f(x, y) = x² - y² + 2xy + 2x…

A: Please find attachment for the details solution

Q: Let f (x, y) and g(x, y) be functions of two variables withthe property that ∂ f/∂x= ∂g/∂x and ∂…

A: Given: f(x, y)  and g(x, y) be functions of two variables with the property that ∂g∂x = ∂g∂x and…

Q: Let f(x, y) = 6x³ – 3e²y + 9y. 8u? – 2v || Assume that y = 2uv. Consider the composite function 9(u,…

A: We have to fund the value of gv(u=-1,v=1).

Q: Evaluate F.dr where F(x, v)=xyi (4, 0).

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Q: Let f(x, y) : V 125 – 3x? – 2y² - Evaluate f(1, 2)

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Q: Let f (x, y) = Vy – 2x Evaluate f(3, 10)

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Q: Show that the function given by f(x,y)= x² + 3xy is differentiable at every poin using the…

A: Introduction: Distinctiveness (differentiability) implies continuity. If a function is…

Q: ) Verify the continuity of the function f(x, y) 26– 2x -- y at the point (2,-3).

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Q: Let F(x, y, z) y³ 2:5 . What is the value of div F at (1, 2, 3)?

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Q: Let f(x, y) = x³ + y³ + 3x²y + xy + y². Find fæ, fy, fax, fry, fyy.

A: The given function is,

Q: (4xy) w = 3 sin (4xy tan (z) +4 In (5yz)- 8 e

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Q: Let f(x, y) : = x/Y Evaluate f(3, 4)

A: We need to evaluate f(3,4) To evaluate we need to plug in 3 for x  and 4 for y

Q: 5 B) Find y" for the function y = x + Vx at p(1,3)

A: Given query is to find the double derivative of the expression at point p.

Q: | (4z + 4y + 4+8zy) dA where R= [1,2] x (0,1]. R Let I Find

A: Given: ∬4x+4y+4+8xyddwhereR=1,2x0,11

Q: Let F(x, y) = . Evaluate (3,2) SF.. (1,-1) F.dr

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Q: Let F = (2xz+y², 2xy, x²+1), if Vf= F, find f(1, 1, 1) – f(0, 0, 0)

A: Given vector funtion and

Q: X+Z+3Siny X +2y-2

A:

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.