Let f(x, y) = x4 + 3xy° – xy. Use the dropdown menus to choose the option that makes each of the given statements true. • (0,0) is of f. Click for List • (0, ) of f. is Click for List Click for List of f. si (o ) • f is Click for List convex but not strictly convex strictly convex neither convex nor strictly convex

Q: Find a if f(0) = 1, f(;) = }, f(1) = 2 and f(}) = f(}) = a give o f(x)dx = using the composite…

A: Disclaimer: Since you have asked multiple questions, we will solve the first question for you. If…

Q: x+y If Z = x.n. f (***), then show that: X. Zx + y.Zy = z

A:

Q: Let f(x, y) = x* + 2x² – a – ay + y² – 5y and let D be the closed rectangle with 0 < # < 5 and 3 <…

A:

Q: 13. If y (x, t) is a function of x and t, prove that i) L. =py (x, p) – y (x, 0) 2. ii) L =p°y (x,…

A: By Bartleby policy I have to solve first 3 subparts

Q: Let fn(x) = E s;(x) Y; be a linear smoother. Find a condition on the weights s;(x) so that fn(x) is…

A:

Q: Suppose that P1(t), p2(t), and p3(t) are continuous on R, and that y1, Y2, and y3 are solutions to…

A: Wronskian of the function

Q: Let f(x,y) = x² – 8x + 2y² + 4y + 7. a. Find and classify all critical points of f.

A:

Q: Find the minimum and maximum values of the function f(z,y, z) = 3r # 2y + 4zsubject to the constramt…

A:

Q: Evaluate f(x, y, z) dV for the specified function f and box B. f(x, y, z) = z3; 13 x < 8, 1 S ys 5,…

A: Given

Q: is concave up on interval The graph of f(x)= x2 – 1 OA(-1,1) OB (0,1) oC(-1.0) U (1, 00) OP (-x,-1)U…

A: F is concave up if f’’(x) &gt; 0.

Q: The domain of the function f (x, y, z) = In(6 - 3xy) %3D is {(x, y) E R? : xy 2} {(x, y, z) E R :…

A:

Q: Let f(x, y) = x³ + y³ - 2x²y². Calculate fa, fy, fax, fyy and fry. Hence show that (3/4, 3/4) is a…

A:

Q: If Wly, , y2. Yal = 0, then (y1, y2 , y3) must linearly dependent, where y1, y2 , y3 are…

A: Given that if  W[y1,y2,y3]=0, then {y1, y2,y3} must linearly dependent, where y1,y2,y3 are…

Q: x - y -2x Prove by definition that for f(r, y) fy(x, y) = %3D x+ y' (x+ y)2

A:

Q: Given the function: f(x,y, z) = x°y2² + æy° +y°z Find а. fazy: (x, y, z) b. fazyz(1, –1, 1) -

A: Given the function :  f(x,y,z) = x3y5z7 + xy2 + y3z

Q: Suppose that f(x, y) : at which {(x, y) | 0 < x < 4, – x < ys va}. 1+ x D

A: Consider a given function:  The objective is to evaluate the following double integral of fx, y…

Q: Show that the function u(x,t) = t/2e-*/4 (t > 0) satisfies u, = uxx.

A:

Q: The function f(x) = Ei-1 Cix;| is piecewise linear and convex. True O False

A: Step:- 1 Convex piece-wise Linear: - A function f: ℝn→ℝis a convex piece-wise linear if there exist…

Q: 2. Show that the function u = p(xy) + Vry ý(y/x) provides the equation n, = 0. dy? U -

A:

Q: Given a function f(x,y,z) = 5x² In (7y + 3z). Find the domain of the function. %3D o {(xy,z) |z >…

A: Use logarithms definition to choose the correct answer.

Q: 5. Let F(x, y) = x² + y² + xy + 3. Find the absolute maximum and minimum values of F on D = {(x, y)|…

A: The main objective is to find absolute maximum and minimum of f(x,y) subject to given condition.

Q: (b) Let f(x, y) ax² + bx²y + cy2 + d with a, b, c, d 0. By calculating fx, fy, fxx, fyy and fry,…

A:

Q: 3x4 – 4x3 – 12x² + 18 f(x, y) = 12(1+ 4y²)

A:

Q: If f =x-e" and F=x'yi-2y'zj + xy'z'k, find: div(F x grad(yf )) at (4,1,-2)

A: The function                     Then, we have to find

Q: Show that the function f(x, y, 2) = (x² + y² + 2e**)4 is strictly convex on R³.

A:

Q: Calculate of of and for the function f(x, y) defined as : ax' dy sin (xy) 1 + y f(x, y) =

A:

Q: (a) x² + zsen xyz = 0

A:

Q: Thank you!

A:

Q: Q = find of るf and るこ for the Ganction f(xz)-ディズ メ+Z

A:

Q: Let a and b be nonzero and f(x, y) = (ax + by)e-x Show that if a ± b, then there are five critical…

A:

Q: (b) If F = (5xy- 6x )i + (2y– 4x)j, Evaluate [F.dr along the curve C in the xy-plane, y =x' from the…

A:

Q: Find (if any) the relationship between the empty functions u(x,y) = xcos(t²) – ysin(t²), v(x, y) =…

A:

Q: Let f(x,y)=2x²+y²-8x-6y+12. 1- Find Vf at (1,1). 2-Find the extreme values of f.

A: Given data: The expression for the given function is f(x,y)=2x2+y2-8x-6y+12. 1) The given point  is…

Q: The values of fx , f y and f, at (1,1,1) for the function f (x,y,z) = x² + xyz +z are fy= Choose. +…

A:

Q: Q1. (a) Find the points (x ,y, z) in space, where the function f(x, y,z) = /x² +y² -1 Is continuous.

A: Given :- The points x,y,z in space , where the function f x,y,z = x2 +y2 -1 is continuous.

Q: Determine the linear approximation of f(x) = x* at x = 1. а. у %3D 4x - 3 O b. y=- 4 x - 3 О с. у-…

A:

Q: Let f(r,y) r+ 12ry+12y. Find all the critical values and claesify them.

A:

Q: If z=f(x,y), x= r cos θ and y= sin θ, where f is a differentiable function expressing az/ax and…

A:

Q: B. Suppose that Z = f(x.y) is given implicitly by an equation F(x.y.z) = 0. Prove that dz/ax =…

A:

Q: 4. For the function f(x, y) = exp (ax + by) find the maximal possible value of the directional…

A: In this question we will use basic of calculus i.e concept of vector calculus. We will find the…

Q: Obtain the function x to minimize the following functional. x(0) = 2, x(t,) = 5 – 4t

A:

Q: the function 2x4jwhen x²+y°+0 Prove that h (a,y) %3D Oj when x=y=0 epect is Variables Lontinuous…

A:

Q: 2. Let f(x,y) 3x y. If C is the line segment from (1,1) to (2,3), evaluate r'dt.

A:

Q: Find the Wronskian for the set of functions.{x, x2, ex, e−x}

A: Given information: x, x2, ex, e-x The Wronskian is given by the following determinant.…

Q: Which of the following is a parameterizatino of the line that passes through the point (5, 4) with a…

A: Given query is to find the correct option for the line.

Q: Find and classify all critical points of the function 5 f (x, y, z, w) = x² + y? + 3z2 + w² + 3xy+…

A: The given equation is f(x,y,z,w)=x2+52y2+3z2+w2+3xy+6xz+5xw+4yz+2yw+5x-3y+6w. The partial is…

Q: if (x, y) # (0,0) (1 if (x,y) (0,0) x+y (a) Prove that the function f(x, y) =2x+y is not continuous…

A:

Q: Let ƒ (x, y) = x² - y² . Find all all points (x, y) such that Vf(x,y) =±(1, 1).

A: