QI a) Find the max relative error when we evaluate the function f(x,y) = Jx² – y at 10-4 the point P(25,49) for Ax = Ay = -

Q: (a) Find the points (x ,y, z) in space, where the function f(x, y, z) = Vx² +y -1 Is continuous.

A: It is well known that the equation z=x2+y2 represents a circle with centre at the origin. The…

Q: 1) Using the linear approximation of the function z = g(x, y, w) = xy³w² – 2x³ + e" + 5 around the…

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Q: z=f(x, y) =2 x +3 y at the point (2, 2, 20). (ii) Use a linear approximation to estimate f(2.1,…

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Q: (a) Find a function f(x, y) with gradient F, where F = (y cos(xy), x cos(xy) + y² + 2y) (b) Use your…

A: Solution of given question is followed by:

Q: ind the value of x at which F(x) = S(t|+2) dt %3D 3 akes its minimum value on the interval [4, 60].

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Q: Find the linear approximation of the function f (x, y, z) (3, 2, 6) and use it to approximate the…

A: Given that  f(x,y,z)=√(x^2+y^2+z^2) To find the linear approximation of f(x,y,z) and also find the…

Q: Let f be a differentiable function of one variable, and let f(p), where p = (x² + y² + z²)'/2. Show…

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Q: Find the linear approximation to the equation xy f(x, y) 2. at the point (4,6,4), and use it to…

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Q: Find the linearization L(X,Y) of the function  f(x,y)=y-1/x+1 at(0,0).

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Q: Evaluate F dr, where C goes along the curve {x* + y* = 1, z = 2} from (1,0, 2) to (b) (0, 1, 2).

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Q: The function f(x, y) = x2 – y² at the point (0,0) is saddle point. صواب İbi

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Q: Find the linear approximation to f(x, y, z) = at the point (–2, 3, 2) f(x, Y, z) ×

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Q: 2) f(x, y) = x +y on the closed triangular plate bounded by the lines x 0, y= 0, y+2x = 2 in the…

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Q: Find the linearization of the function f(x, y) 155 – 2x2 – 5y² at the point (5, 4). L(x, y) = Use…

A: Given:      f(x,y) = √ (155 - 2x2 - 5y2 )     Point : ( 5 , 4 )  Now     Linear approximation f (…

Q: Find the linear approximation of the function f (x, y,z)= x' Vy +z° at the point (2, 3, 4) and use…

A: Given:-               Find the linear approximation function f (x,y,z)= x 3y2+z2 at the point…

Q: Q3A) Find normal line and parallel plane to the function f(x, y, z) = x²y²z² - 4 At point (1,-1,2).

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Q: Evaluate F.dr where F(x, y) = xy i+ej and Cis the line segment from (2, 0) to (4, 0).

A: From Stoke's theorem:   ∫CF·dr=∫F1dx+F2dy+F3dz   Given: Fx,y=xyi+exjLine segment;2,0to4,0

Q: Find the linear approximation to f(x, y, z) = at the point (2, –1, –2): f(r, y, z) z

A: A Givenfx,y,z=xyz at the point 2,-1,-2linear approximation at the point…

Q: Q4: Find fz for f(x,y, z) = xcos(y + 3z) + xyz at the point ( 1,3,-1) %3D

A: Consider the function: fx,y,z=xcosy+3z+xyz. Find fz at 1,3,-1. Since fz=∂f∂z. Calculate partial…

Q: Find the linear approximation to f(x, y, z) = " at the point (2, -1,1): f(x, y, z) z

A: Given the function

Q: f(r, y, z) = sec='(9x + 3yz) f. = fy = f; =

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Q: 1. a- Find a result by using variable separation for ý=secy h- xy = x + y

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Q: c) Let f(r, y) = Vlry| Prove that f(r, y) is not differentiable at point (0, 0).

A: Given a function : f(x,y)=xy We need to show that f(x ,y) is not differentiable at (0 ,0). Let's…

Q: Answer the question below: x+y The student should find the local linear approximation of f(x, y, z)…

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Q: f the joint PDF of X,Y and Z is xyz? fx.x.z (x,y, z) = 0<x<1,0< y < 2,0 < z < 3 9. 0, otherwise

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Q: Using linear approximation of f(x,y)=*+Y at (3,2), the value of f(2.94,1.94) estimated to be x-y

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Q: (a) Assume that traffic flows at a rate of 240 vehicles per hour on the stretch of road between…

A: The number of vehicles coming and leaving the signal is same in all the signals. That is, Total…

Q: (e) Find the linear approximation of the function f(x, y, z) = x³ √√y² + z² at the point (2, 3, 4)…

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Q: Find the linear approximation to f (x, y, z) = 3, -3, – 1): at the point | F(x, y, z) ×

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Q: Let f(x, y) = 2x^3+5y. Find the linear approximation of f(x, y) near (1,5), and use it to estimate…

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Q: (b) Let z(r, y) = exp(-|r|) cos r + y², where r + y /9 = 1. Show that z(r, y) has minimum points…

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Q: Integrate f(x,y,z) = x-3y + z over the line segment joining the points (0,0,0) and (2,2,2). %3D

A: Here, we need to integrate f(x, y, z)=x-3y2+z over the line segment joining the points (0, 0, 0) to…

Q: Consider the function f(x, y) = 3x? + ry + 2y? Use the linearization of f(x, y) about (1, 1) to…

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Q: Find the linearization of f(x,y) at the indicated point (X0,Yo): f(x,y) = In (x² + y); (1, 1) L(x,y)…

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Q: Find the linear approximation to f(x, y, z) = at the point (3, -2, -2): f(x, y, z) Z

A: To find the linear approximation of the below function at the point 3,−2,−2. fx,y,z=xyz

Q: Let X and Example 20. PDF 0<I<3, 0<yS3 fxy(r, y) = otherwise Find

A: Hello! As you have posted more than 3 sub parts, we are answering the first 3 sub-parts.  In case…

Q: Find div F if F(x, y, z) = (x² + y)i + z²j + (eY - z) k.

A: Our Aim is to find the value of div F if F(x,y,z)=x2+y i +z2 j+ey-zk -(i)Let  F(x,y,z)=x2+y i +z2…

Q: Find the linear approximation of the function f(x, y, z) = V x² + y² + z² at (3, 6, 2) and use it to…

A: Given: f(x,y,z)=x2+y2+z2 at (3,6,2)find f(3.01,5.98,1.97)=3.012+5.982+1.972

Q: Find the linearization of f(x,y) at the indicated point (Xo,Yo). f(x,y) = /x +2y; (4,7) L(x,y) =

A: Given:- f(x, y) =√x+2y To find:- linearization of f(x,y) at the indicated point (xo.Yo). f(x,y)=√√x…

Q: Exercise I f(1, y)yz (a) Let f(r,y) = rỷ - . Then deduce that f(1,y)zy (Clairaut's theorem). %3D

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Q: 2. Use suitable linearization to find the approximate value for the function at point P. f(x,y) (x-…

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Q: use linear approximation to give an estimate for the value of g (0.97, 2.01, 3.02) given g (x, y, z)…

A: Linear approximation of a function : The linear approximation of a function f(x,y,z) at some point…

Q: Find the linearization of f(x,y) at the indicated point (Xo.Yo). f(x,y) = In (x +y): (4, 5) L(x,y) =

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Q: f(x, y) = Vx + y³. Estimate f(7.96, 2.01) by finding the linear approximation of f(x, y) at (8, 2).

A: we have to find the linear approximation of f(x,y) at (8,2)  and then estimate f(7.96,2.01) the…

Q: (a) Find a function f(x, y) with gradient F, where F = (y cos(xy), x cos(ry) + y² +2y) (b) Use your…

A: (a)According to question given :F→=y cos(xy), x cos(xy)+y2+2yWe have to calculate for f(x,y)As we…

Q: z=f(x, y) = 2x +3 y at the point (2, 2, 20) (ii) Use a linear approximation to estima

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Q: Q.1 The natural domain of fur f(x,y) = lnx² + Iny is а) {(х, у):х > 0, у > 0}

A: Log function is defined for positive values

Q: dw Evaluate at (u,v) = (5,3) for the function w(x.y) = xy² - In x; x = e" +V, . y = uv.

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Q: Find the linearization of f(x,y) at the indicated point (X0:Yo). f(x,y) = In (x +y); (6, 1) L(x,y) =

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Q: Find the linearization of f(x,y) at the indicated point (X0.Yo)- f(x,y) = /x + 2y; (1,6) L(x,y) =

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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.