3. Find all functions from X = {a,b} to Y = {p,r, t}.

Q: Compute the values of dy and Ay for the function y= e4z + 5z given z = 0 and Az = dz = 0.02.

A: Given x = 0, dx = ∆x = 0.02            (1) Here y = f(x) = e4x+5x

Q: Calculate D(fog) for the functions f(x, y, z) (st, tu, su).

A: answer is in next step

Q: 3. Find fz and fy where f(x,y) = In(x + y²).

A:

Q: Suppose that a = x(t) and y = y(t) are both functions of t. If a² + y} = 29, %3D and d = 1 when a =…

A: The given equation is x2+y2=29. Now find the derivative dydt, when x=5, y=2 and dxdt=1as follows.

Q: Use e – 6 definition and show that the function 4x² – y? if (r, y) # (1, –2) 2r + y f (r, y) = • 4,…

A:

Q: 3. Find , 9 for the functions: ax' ây sin(x³ + y* ) x* +y , (x,y) = (0,0) f (x.y) = .(x.y) = (0,0)

A: f(x,y)=sinx3+y3x2+y2, x,y≠(0,0)0, (x,y)=(0,0)

Q: Let f(x, y) = ln(x + y − 1). Then, ƒ(e, 1) =

A:

Q: Find the linearization L(x, y) of f(x, y) = x2 y3 at (a, b) = (2, 1). Use it to estimate f(2.01,…

A:

Q: Determine dz for z = f(x, y) = e^(x^2+y^2) if x changes from 1 to 1.02 and y changes from 2 to 2.1.

A: use formula :-    dz = fx(x,y)dx + fy(x,y)dy

Q: af Find a d () + In (). of the function f(x,y) = arccot and ду

A:

Q: 2²y. 3. Consider the function f(, y) =

A:

Q: 4. Find if y is a function of r defined implicitly by da 2*y + sin a = xe" + In

A:

Q: : Express the function f (x) = e") to the form u(x,y) + iv(x,y).

A:

Q: 19 Let y be a function such that y(1) , where Y (s) = L{y (t)}. If it is known - that: d ds s4…

A:

Q: Find for following 1.y = (x + v3x)S

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

Q: Find the linearization L(x) of the function at a. f(x) = Vx, a = 25 L(x) =

A: The solution of the problem is given in the next step.

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: For the given function 9 = x-yz and 62 -(@C) at C= 3x?yi+ yz²j- xzk, Find 5yöz бубz point (1, – 2, –…

A:

Q: 4. Let f(x, y)=2x*y' . Find f,(x,y)

A:

Q: 2. Show that the function u p(xy) + Vry (y/x) provides the equation = 0.

A:

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

A:

Q: 4. Suppose that F(t) is a differentiable function of one variable. Define the function z(x, y) = e'F…

A: z(x,y) ey F (exy )diff wrt xdzdx = ey F' ex/ye.1/yzx = ey.ex/yyF' (ex/y)and diff wrt ydzdy= ey…

Q: 2 3 tegral of the function xy d by x = 0, y = 0, z = C %3D %3D (2(5)

A:

Q: 3. Evaluate f 2xdx + (y + 2)dy along the rectangle with vertices (0, 0), (0,3), (3,3) and (0, 3).

A:

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 y = x¹/², x > 0, is strictly concave

A: Given that y=x1/2 Differentiate both sides w.r.t x, y'=12x1/2-1y'=x-1/22 Again differentiate w.r.t.…

Q: 7. Find function q(z) = x³ − 3xy² + iv(x, y) is analytic, find v(x,y).

A: if a function is analytic then C-R equations satisfy.

Q: Eliminate the arbitrary constants a. x = -In t, y = at + bt?

A:

Q: 17. Let f(x, y) = x'y4. Use Eq. (4) to estimate the change Af = f(2.03,0.9) – f(2, 1)

A: You have to just put the value in the function and proceed....go through the solution

Q: Solve the problem. du at (x, y, z) = (1, 4, 2) for the function u(p, q, r) = pq-r, p = y - z, q =X+…

A:

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: Find the linearization of f (x, y)= e²"¬*, at (0, 7 / 2).

A:

Q: Show  that the function Z =1/2(eysinx - e-ySin(x) satisfies the La Place’s equation  =0

A:

Q: 1. Integrate the function f(x, y) = x – y over the triangle T with vertices (0,0), (1,0), and (1,2).

A: Given triangular region is bound by the vertices 0,0, 1,0 and 1,2. The sides of the given triangular…

Q: Find the linearization L(X) of the function at a. f(x) = Vx, a = 16 L(x) =

A:

Q: -2 In(x) Consider the function f(x, y) 3y

A:

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

A:

Q: find the length of the function over the given interval x=2y, y=-1, to y=1

A:

Q: The slope of the secant line of the function y =Vx +x through the points x, = 1 and the point xz = 4…

A: y=x+x

Q: Suppose z = ƒ(x, y), where x and y are functions of t. How many dependent, intermediate, and…

A: It is observed that z=fx,y is function of x and y.

Q: Let C(x) be the cost to produce x batches of Complete parts (a) through (d) below

A:

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: 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: 3. Suppose that z = f(x, y) is a differentiable function with respect to variables !! x and y and is…

A:

Q: Show that the function d: RxR → R defined by d(x, y) = √x-y

A:

Q: Integrate the function f(x, y) = x – y over the triangle T with vertices (0,0), (1,0), and (1, 2).

A: Evaluate : ∫∫T(x-y)dA        ......(1) ∫∫Tx-ydydx T is the region enclosed by the triangle. Region…

Q: Find f(3,4) for f (x, y) = In(x + /x² + y²). %3D

A: Given:- f(x, y) =ln(x+√(x2+y2))  To find:- fx(x, y) at (3, 4)

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: 2. If f(x, y) is a function of y only, then S" S fdxdy Si fdy. %3D

A: Given query is to find statement is true or false.

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

A:

Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.