etf: (0, 1] × [0, 3] → R be the function defined by f(x, y) = x' + 3y and let E be its graph. The value of 5x + 2y do is e integral EV1 + 9x* + 36y2

Q: (2) Let F(x, y) = (cos(y)+2x, -x sin y+1). Show that F is path independent by finding %3D a…

A: For the given vector function to be independent, it must be derived from a potential scalar function…

Q: 4x Find the linearization L(x,y) of the function f(x,y) = e cos (5y) at the points (0,0) and 0,

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Q: Find the linearization of the function f (x) = x at a = 1. a Va lal sin (a) L (1) Using this…

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Q: et f(x,y) be a function whose partial derivatives exist and are continuous at a point (a, b). Which…

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Q: b) Show that the “energy function" E(x, y) = 5 + is non-increasing along the solution, i.e., using…

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A: According to the given information, consider the given function z.

Q: The curved surface of a rod of length L is perfectly insulated against the flow of heat. The rod…

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Q: 3. Find the total differential of z = f(x, y) if z2 - y = (1– 2x)z.

A: Total differential of a function z=fx,y is dz=∂z∂xdx+∂z∂ydy

Q: Given (x+ y}* – ( x - v}² = x* + y^, find dy/dx using implicit differentiation. A. - 2- E. None of…

A: Given x+y2-x-y2 =x4+y4. We have to find dydx  using implicit differentiation.

Q: 5.) Suppose z = f (x, y) , where x=x(t,r) and y= y(t,r). Assuming all the functions involved have…

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Q: a. w = √√x² + y² + z² xy b. w = x+y+z c. w = In√√x² + y² + z² 1

A: Use the procedure of partial derivatives to find with respect to x y and z as in next step.

Q: 7. ( ) The surface area of the surface S with equation z = g(x, y), where (x, y) lies in D and f has…

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Q: Consider the finction f(x, y) = 6y² + 4x² – 12xy- 4y. Then: (1,1) is a critical point and f has a…

A: The given function is f(x,y)=6y2+4x2-12xy-4y

Q: The Wronskian of two differential functions f and g is W(f.g)=fg'-gf, more formally, f(x) W(f,g)(x)…

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

Q: 5. Determine a function v(r, 0, ø) with Av = 0 _in B2 \ B1 satisfying the boundary conditions v(1,0,…

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A: Given 1+3xsin ydx-x2cos y dy=0....(1) with y1=0 We will find the value of fx, y to approximate y

Q: Let z be defined implicitly as a function of x and y by the e e-zy əz find O UTM + cos (xy) = (4 –…

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Q: Let F(x, y, z) = (2x cos(y), e² – x² sin(y), ye²). (a) If possible, find all potential functions for…

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Q: b) Obtain all the first and second order partial derivatives of f(x,y, z) = e* sin In yz + e sin In…

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Q: Show complete solution. Expand, that is, perform the indicated operations on the differential…

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Q: 2) Let 1 = f* cos y3 dydx. By reversing the order of integration of I, we get a. 1 = ²₂x cos y³ dx…

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Q: Find the first partial derivatives of the function a) f(x, y) = x*y-2 – 4xy + e7y + In (2x) b) c =…

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Q: 4) Find f, fy and f, for the following i) f(x,y,z) = sin-xyz ii) f(x, y,z) = y z In xy iii) f(x,y,z)…

A: Note:  Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the…

Q: 1. Let, z=sinx cosy, where x=s+t, y=s-t, and z=x?+y', x=sin(st), y=s?t', az аnd əs az Determine the…

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Q: 1. Find of/ar, af/ay and of/0z (y- sin(x))² f(x, y) = (r - 1) (y+ 2) + S(1, y) = in(V + y²) + (z² +…

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Q: The function f(x, y) = L(x, y) = arctan(x + 2y) can be approximated by the linear function = ax + by…

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Q: find the first partial derivatives of the function f(x, y) = integral from y to x of cos(t^2) dt

A: the given function is , f(x,y)= ∫xycos(t2)dt

Q: Let w = x°e4y cos(9z). Find the value of dwldt at the point (3, ln 5, 0) on the curve x = 3 cos(t),…

A: Given: w=x6e4ycos(9z)x=3 cos(t)y=ln(t+5)z=6tDifferentiating we…

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Q: A) If w = 2 y et* – In z where x = In(t² + 1), | dw y = tan-1 3t and z= e3t. Find by Chain Rule dt

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Q: e) Suppose that W= √√x² + y² + z², x= cos 0, y = sin 0, z = tan 0. dw T Use the chain rule to find…

A: According to our company's guidelines I can only answer (e), since (e) and (f) are not inter…

Q: Let f(x, y,z) = x² sin y + y e², where x = t + 3,y = net-1 and z = ln 2t. %3D df at t = 1 is: dt…

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Q: Using an appropriate linearization, the local linear approximation of f() = T+ cos z at COS I is -…

A: Use linear approximation

Q: 1. If z = f(x, y) has continuous second-order partial derivatives and x = r cos 0, y = r sin 0,…

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Q: Given function f(x, y) = 1+ xy - x - y. df a) using partial differential involving limits to obtain…

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Q: 1. Let z = f(x, y), find for: and dy - - (a) e"y + z ln y = 0 (b) yz – sin z = xy

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Q: Consider the IVP S2(t) = -1+cos(t + x(t)) cos(t + x(t)) x(0) = 0. Show that the ODE is exact and…

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Q: an f (b) For a positive integer n, find the n-th partial " azn derivative off with respect to z, for…

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Q: A:= {(x, y) € R² :1< log(x) < 2}. = {(x, y, z) E R³: sin(xy² + «/2) · cos(z) = 1} . (a) Decide…

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Q: 4] I Let w = 5 cos(xy) – sin(xz); x = 1/t, y = t, z = dw using an appropriate form of the chain…

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Q: b- Use Chain Rule to compute w = 2y e* - Inz } əw at x = ln(t² + 1), at (t) equal to (1) for: y =…

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Q: se Euler method to compute ys for the DE yy'=2 x for y(1)=3

A: Euler's Method

Q: 1. if z = a² sin[e!n 2y] + 3xy cos[e!n2x] – 4a?y², find the partial derivative of z with respect to…

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Q: Compute the partial derivative of the function f(x, y, z)= el-x cos(y) + ze=1/(1+y²) with respect to…

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Q: Q2 (a) Find the first partial derivative of (i) f(x, y, z) = (ii) f(x,y,z) = e% cos xy (b) Solve and…

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Q: of at (r, s) = (1,0), where ds Use the Chain Rule to evaluate the partial derivative f(x, y) = In…

A: Solve by partial derivatives

Q: What is the partial derivative dv/dy of the following function? v = 3x + 9xy -y/In(z) + cos (z + x)…

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Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.