Determine whether the function t(xry, 2)=x' +y-2 (where Y,/ and Ź are s tritly greater than 0) is concave or convey.

Q: ive of f(x, y, z) 1) in the dired

A:

Q: Find the derivative of the function f(x,y,z) = x² + 2y² – 3z² Po = (1,1,1) in the direction of at…

A:

Q: What is frz, fyy, and fyz of f(x, y) = In(y²")?

A: Given:           f(x,y)=lnyx2          fx=∂∂xlnyx2         Treating y as constant variable…

Q: Find the local linear approximation to f(x) = Vx at x = 1 and use it to approximate both 1.1 and…

A: To know which one is better we have to compare with calculator values of sqrt(1.1)  and sqrt(0.1)

Q: Express in form y=f(x) by eleminating the parameter x = t + 3, y = 4t

A:

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

A:

Q: Find the diectional derivative of the function f (xiy,z)= sin (xy+2) at the point of P(1, al2 x4) a…

A:

Q: Differentiate f(x) with respect to g(x) of yx=xsiny

A:

Q: Find the derivatie: F (+2 %3D (-t*+*z+)た =人

A:

Q: Find the linear approximation of the function f (x, y) y- 1 at (0,0) x + 1

A: We are given fx, y=y-1x+1. Here, we need to find linear approximation at (0, 0). Now, fx=∂∂…

Q: Solve ux – uy +yu = 0, where u is a function of x and y. %3D

A: Given: ux-uy+yu=0. The objective is to solve u, where u is a function of x and y.

Q: Find the linearization of the function f(x, y) = /36 – læ² – 2y² at the point (3, -1). L(x, y) = Use…

A:

Q: Find the point where the CAUCHY- RIEMANN equation is satisied for the function f(2) =xy+Xyi

A:

Q: Find all values of x, xe[0,2n] where f(x) = secx has a horizontal tangent line

A:

Q: Consider the function f(x) = 3z10 + 3z° – 3z² – 4. Enter the general antiderivative of f(z)

A: Given function is : f(x)=3x10+3x5-3x2-4 We have to find antiderivative(integral) of the given…

Q: Find the linearization of the function a) z = cos(sin y – x); at (-2,0) and use it to approximate…

A: Suppose f(x,y) be a differentiable function at (a,b). Then linearization of f(x,y) at (a,b) is given…

Q: Let A = {(x,y) = RXR; 0<max{|x-3], ly- 2|}<1}, then: *

A:

Q: of of and ду Find f(x,y) = Vx + 3y?

A:

Q: Find the derivative of the function at Po in the direction of u. f(x, y, z) = In(x 2 + 3y 2 + 9z 2),…

A: Given that      f(x,y,z)=ln(x2+3y2+9z2), P0(3,3,3), u=3i+4j Here we have to find the derivative of…

Q: Find the maximum rate of change of f at the given point and the direction in which it occurs…

A: Consider the function: fx,y,z=xlnyz Differentiating with respect to “x” then,…

Q: Use a linear approximation to estimate f(0,1), given that y=f(X) is a differentiable  with f(0)=1…

A: Consider the given information

Q: Find the linear approximation to the function f(x, y) = sin y --- |T at x, = (1, -2) 2 and use it to…

A: The solution is given as

Q: Show that the function defined by xy √x²+y² f(x, y) {{ = 0 if (x, y) = (0,0) is not differentiable…

A:

Q: What is the derivative of f(x,y) y° at P = (3, 1) in the direction toward %3D Q = (4, –3)?

A:

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

A:

Q: What does it mean for the differentiability of a function if the Cauchy-Reimann equations (Ux = Vy…

A:

Q: Find a linear approximation of the function f(x) = V1-x at a = 0. %3D

A:

Q: 11. Verify that the conclusion of Clairaut's Theorem holds for the function: f(x, y) = exy sin(y)

A: The objective is to verify the conclusion of clairaut's theorm.

Q: What is the domain of the function w = ƒ(x, y, z) = 1/xyz?

A: What is the domain of the function w = ƒ(x, y, z) = 1/xyz?

Q: Compute the derivative of f (x, y) = (y + 2) + xysin(x) at (0,1).

A:

Q: Let f (x, y) = 2x³ + 4y³ + 19xy Find D = frx · fyy - fey at the point (2,2)

A:

Q: prove that xy^2/x^2+y^2 is not differentiable at 0,0 when  xy^2/x^2+y^2 if (x,y) not equal to (0,0)…

A:

Q: Find the linear approximation of the function f(x) = Vr + 15 at a = 1 and use it approximate the…

A: Given, f(x)= (x+15)1/4 a=1

Q: Verify Cauchy-Riemann equation for the function f(z) = z^3

A: To find- Verify Cauchy-Riemann equation for the function fz = z3         Formula Used-…

Q: Let f(z)=ex^2 = U(x,y)+iV(x,y) Verify Ux=Vy

A:

Q: Find fzyz. f (x, y, z) = x°y°z° + xy° + y°z %3D 6-

A:

Q: Find the best linear approximation to f(x) = ex on the interval [-1,1]

A: We have to find the best linear approximation of f(x)=ex on the interval -1,1.

Q: Find the derivative of the function at Po in the direction of A. f(x, y, z) = xy + yz + zx, Po(1,…

A:

Q: 7 For the function eX, the linear approximation around x = 2 is %3D

A:

Q: Verify Young's Theorem f(x,y) = e(2x+y) In(xy)

A:

Q: What is the linear approximation for any generic linear function y=mx+b?

A: Given: y=mx+b

Q: Find the linear approximation of the function at the give f(x.y) = 3x y at (- 6,9) O A. L(x,y) = -…

A:

Q: Determine f„ (0, T, 1), fy(0, , 1), f¿(0, r, 1) given the function z sin(3xz+ y²)

A: The given function,        zsin3xz+y2

Q: 2 f(x, y) = x² + 3xy

A:

Q: Find the local linear approximation L (x)of the function f (x) = lnx at x = 1 %3D

A: LINEAR APPROXIMATION

Q: Find f fy. - f(x.y.z) = x - Vy² + 22? + 2z² = (Type an exact answer using

A: Here we have to find fx , fy and fz  of

Q: At what interval is y=2r4- 4x2 concave upward? U x> 3 x 3 3 <x<- 3 3

A: The given function is y=2 x4-4 x2 We have to find the interval at which the function is concave…

Q: Consider function f(x, y) = x cos(TxYy) + x³y. .3,

A:

Q: Consider the function f(x) = 4x° + 7x® – 9z³ – 10. %3D Enter the general antiderivative of f(æ)

A:

Q: What is the maximum value of the directional derivative of f(x, t) = f (x, t) = x² + t²/8 – 10 at…

A: Note: The directional derivative of a function is the rate at which the function changes at a…