Show that the directiona f(x, y, z) = z²x + y ² at ( X (1/15" + ) ; 255. them

Q: find extreme Value of function fex, y) = x°t 3xy?-3x²-3y=t7 1

A: Given:  fx,y=x3+3xy2-3x2-3y2+7 ⇒fx=3x2+3y2-6x, fy=6xy-6y To find extreme points put fy=0, fx=0…

Q: az/ Find az/əx and of the function: dy r* z2 – 5xy z = x² + y³

A: Given: x3z2-5xy5z=x2+y3 To Find: ∂z∂x=?∂z∂y=?

Q: 2y)j + x the point

A:

Q: dy if y= 3x Find dx х2+1 3(1-х2) D) (x2+1)2 3x2-3 A) 3. 3 B) 2x C) (x2+ 1)2 х2 +1

A:

Q: -t,x-1 dt

A: Please see the explanation below

Q: Let C z-1=3 and1 = §, = dz. Then

A: The solution is given as

Q: Find f, (2,0) if f(x,y) = 18x e Y. 1,(2.0) = %3D

A:

Q: Find mZX (3y-71° X Y (2x) O W (x+181° (3y + 1)º

A: Solve for the angle X

Q: Find &, for f(a, y) = xy? – 4.ry² +x*. 3

A: This question is related to partial derivatives.

Q: Find and sketch the domain of z = f(x, y) = In(9 - x - y²).

A:

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

A:

Q: Calculate for w = xyz. By

A:

Q: 3. Which function has a range of yS 3? Ax) -- +3 с. a.

A:

Q: Find y' if 3x2- (xy²) = 2y³ 2 3=

A: Given: 3x2-xy212=2y3   As we know that; The sum/difference rule: f±g'=f'±g' The Power law;…

Q: Verify that ƒxy = ƒyx, for ƒ(x, y) = xey.

A: Given function is fx,y=xey We have to verify fxy=fyx Solution: fxy means that first we find partial…

Q: + y = 2. What is y" at the point (1, 1)? y ² Suppose that x +

A:

Q: Eliminate the arbitrary constants y Iny = C,e "+ C, X-

A:

Q: dx. = 9) Evaluate 2x-1

A:

Q: 2. fote-t² dt

A:

Q: If fxy (x, y) = , ,0 2) =

A: Given,fXY(x,y)=x+y27 ; 0<x<2 , 3<y<5

Q: Find fy (-1,-4,-2) if f(x, y, z) = x³ z4 + 2xy – y? z + 1.

A:

Q: Prove that if x+y=%30 then y=-x

A: See the attachment

Q: find the derivative of (2³ + j)² O 23 +j O 223 + j O 625 + j6z² O 325 + j3z?

A: Derivative of (z3+j)2 is 2(z3+j)2-1(3z2+0) = 2(z3+j)×3z2 = 6z2(z3+j) = 6z5+j6z2

Q: Find the value of x x - 2 x - 1

A: claim- find the value of x

Q: fex)= J4-x +2

A: The function is given by f(x) = 4-x + 2 To evaluate : The graph of the function f(x)

Q: For the given function 6=x²yz C=3x²yi+yz²j-xzk and Find 82 Sysz (c) at point (1, -2, -1).

A:

Q: If f.(x, y) = 13x + 8y + 11, || f.(3, 2) = a. b. f„(5, 2)

A: Given, fx(x,y) = 13x + 8y + 11 a). fx(3,2) = 13*3 + 8*2 + 11 = 39+16+11 => fx(3,2) = 66

Q: Wallis is seated on the line tangent to y=4-3x-x2 at the point (2, -6).

A: wallis is seated on the line  tangent to curve   y=4-3x-x2   at point 2,-6

Q: Suppose that Y = Z - X is independent of Z and of X. Show that Y is a constant.

A: Given that Y=Z-X. To show: Y is a constant function.

Q: Consider the function y -62 Which of the following statements is true for y? = ze Oy" = 36y…

A: Given,