D. Let z = f(x, y) = VI+ 2y+1 a) Compute the local linearization (z = L(x, y)) of f at (0,0). b) Quadratic approximation (z = Q(r, y)) to.f centered at (0,0). c) Compute the linear and quadratic approximation to f(0.1,0.15) (to 4 decimal places) and compare to the actual value.

Q: Let  f(x, y) = sin(15x2 + 3y2) Calculate the quadratic approximation of f at the point (0,0)

A: Given that,  fx, y=sin15x2+3y2 The quadratic approximation of the function fx, y at the point x0, y0…

Q: 3. Calculate the directional derivative of the function f : R³ → R, defined by f(x, y, z) = y²+xz at…

A: Step 1: Step 2: Step 3: Step 4:

Q: c) Given the scalar function p(x, y, z) = x²e - y³ + cos 2z. Find the directional derivative of p(x,…

A:

Q: Find the f(z) = u(x, y) + j v(x, y) for which X b) u = e cosy most general analytic function

A:

Q: Find the linearization of the function f(x,y) = V9x² + 16y² at the point (1, 1), and use it to…

A:

Q: 2. Determine the directional derivative of o(x, y, z) = re" + y² + xyz at the point (2, 0, 3) in the…

A:

Q: (a) Find the direction for which the directional derivative of the function f(x, y, z) = √√x² + y² +…

A:

Q: Let f(x, y, z) = 5x³ - y³ + z². Find the maximum value M for the directional derivative at the point…

A: Our objective is given below:

Q: Find the linearization of the function f(x, y) 155 – 2x2 – 5y² at the point (5, 4). L(x, y) = Use…

A: Given:      f(x,y) = √ (155 - 2x2 - 5y2 )     Point : ( 5 , 4 )  Now     Linear approximation f (…

Q: z= f(x,y) ; x= r-s1 , y= r2s and zx(0,-1) = -24 ; If zx(0,-1)=-18, what is the value of the…

A: Given that z=f(x,y),     zx(0,-1)=-24 and  zy(0,-1)=-18x=r-s and y=r2s We have to find zr(0,-1).

Q: a) Find the directional derivative of the function f(x, y, z) = x³ y³ (2z+1) at the point P:(1, – 1,…

A: Please see the explanation below

Q: f(x. y.z) = + xy + yz + Q8) Find the Linearization at (1,1.2)

A:

Q: 6. Let f(x, y) = ln(2x - y²). (a) (b) (c) Determine the gradient of f at the point (2, -1).…

A:

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: c) Given a function $(x, y, 2) = 3x² + In (3y² + 1) + e* cos z. i. Find the directional derivative…

A:

Q: The function f(x, y) = ¿e=y – In(y²)

A: It is partial derivative

Q: 5. Find the linear approximation of f (x, y, z) = x³y² + 22 at the point (2, 3,4). Use this to…

A:

Q: Let f(x, y) = 6x – 2ry and the point M(5, 9). Among all unit directions, there is a unit direction…

A:

Q: Compute the directional derivative of f(r. y) = = at the point (1, 1) in a irection normmal to the…

A:

Q: a) Find the directional derivative of the function f(x, y, z) = x2 y (2z+1)² at the point P:(1, -1,…

A: This question is related to gradient and it's properties.....

Q: Suppose that z is an implicit function of x and y in a neighborhood of the point P = (0, −3, 1) of…

A: Equation of a line passing through point (a, b, c) and parallel to vector <p, q, r> can be…

Q: Find the linearization L(x, y, z) of the f(x, y, z) = 6(x3 + y3 + z3)1/2 at the point (1, 2, 3).

A: f(x, y, z) = 6(x3 + y3 + z3)1/2We have to find linearization L(x,y,z) of f(x,y,z) at point (1,2,3)

Q: Prove that the directional derivative of f(x, y) = y + 2xy³+x²y2 at point (0, 1) in the direction…

A: The gradient is just the vector of partial derivatives. The partial derivatives of f at the point…

Q: 49. Differentiate y = cosh²4x a. 4(sinh 8x) b. 12(sinh 8x) c. 8(sinh 8x) d. 2(sinh 4x)

A: