Find the domain of the function f(t) = V1- 21 – 3Vī+ 6.

Q: Find linearization of the function f(x) = Vx + 3 at a = 1 and use it to approximate V3.98

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Q: Determine an approximate solution of the equation z3 + 3xyz? – 5x²y²z+ 14 = 0 for z near 2, as a…

A: To determine : an approximate solution of the equation               z3+3xyz2-5x2y2z+14=0 for z near…

Q: Graph the function f(t) = (/t, 2t +1) by eliminating the parameter.

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Q: Find d2y/dx2 as a function of t if x = t - t2 and y = t - t3

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Q: For the function ex, the linear approximation around x = 2 is %3D

A: Introduction :

Q: Find f, fy. f- f(x.y.z) = 3x - 4y 2. 2 +z?

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Q: The function f(x, y) = -3y + 2√√ry is a

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Q: Q3): Does the function r(x, y) = xs -xay² is harmonic?

A: As we know that; the function fx,y is harmonic. If ∂2f∂x2+∂2f∂y2=0 or fxx+fyy=0 Given:…

Q: Consider the function f(x) = a²e15z. f(x) has two inflection points at x = C and x = D with C < D…

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Q: Q1. Find the maximum and minimum values of f? (Using Graphical Method) f = 10x + 28y Subjected to:…

A: Consider the given function. fx,y=10x+28y And, the subject is defined as, 5x+5y≤1502y-5x≤2y-10≤7…

Q: Find the domain of the function f(x,y)= exy/ x-y2

A: Answer-

Q: Find all stationary points of the function z = f(x, y) = 3x² – 6xy + 2y³.

A: To find stationary points of the function z=fx,y=3x2-6xy+2y3

Q: Q1) Find the local extreme values of the function f(x, y) = 3y2 - 2y - 3 x + 6xy

A: We use second order partial derivative to find maximum, minimum and saddle points

Q: Find the maximum and minimum values of the 2x3 function f(x,y) = * - 2xy – 5x + 2y² + 4y + – 2xy –…

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Q: Use the EVT to find the maximum and minimum values of the function f(x, y) = e4a-5 yʻ on the disc x²…

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Q: Maximise the function f(x, y) = 4xy² subject to r + y? = 2.

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Q: Consider the function z = ƒ(x, y) = 9x3 - 8x2y + 4y3.;Find dz.

A: Consider the given function, z=fx,y=9x3-8x2y+4y3 The formula of the total derivative dz is,…

Q: f(x, y) = 4x² – y²

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Q: 3 ) Express f(t) in terms of the unit step function u(t).

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Q: find the specific function values. ƒ(x, y) = x2 + xy4 ƒ(-1, 1)

A: Given: fx,y=x2+xy4, f-1,1 for finding given value we substitute x=-1, y=1 in given expression

Q: Consider the function f(x) = 2x³ + 71° – 8z2 – 8. Enter the antiderivative of f(x) + C

A: To find the antiderivative means integration of the given function

Q: For the function f(x,y,z) = 3 + xy5 - 5z4, find fx , fy , and fz.

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Q: For the function y = f(x) = x² – 2x, x x ≥ 1, find (ƒ-¹) '(3) = df-1 dy y=3

A: We have to find the f-1'(3).

Q: ) Find the local linear approximation of the function f(x) = V1+x at xo = 3, and use it to…

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Q: Find the domain of the function:f(t) =∛(t + 4)

A: Given function is: ft=t+43 We have to find the domain of f(t).

Q: Draw the domain of the function: f (x, y) = Vx² + 9y² – 36

A: Please refer the attached image for complete solution. THANKYOU.

Q: d²y 2. Determine of the function y = dx2 x²cos (x)

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Q: Find the linearization of the function f(x, y) = V61 – 3x2 - 1y? at the point (4, 2). %3D L(x, y) =

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Q: Find fryz from the functions f (x, y, z) = 4x³y² – e²y* + + 4y – x16

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Q: Find whether the function F-(* - y')i + (v² – 3x)j + (=* - xy)k is irrotational.

A: A vector field F is called irrotational if curl (F) = 0.

Q: Find the absolute maxima and minima of the function f (x,y)=2x²-4x+y²-4y+1 on the closed triangular…

A: Given:The given function is f(x,y)=2x2-4x+y2-4y+1 on closed triangular region bounded…

Q: Find all local extrema for the function f(x.y)= 4y-128y +3x -11.

A: Given,  f(x,y)=4y4-128y2+3x2-11

Q: 2. Find whether the function F-(* - y' )i + (v² - 3x)j + (:² - xy is irrotational.

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Q: 3. If f(x) = [ v19 +r² dt , find f'(3).

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Q: Find the domain of f(x, y) = Vy+I y(1-x²)

A: Given: f(x,y)=y+1y1−x2 The domain of functions of two variables, f(x,y) are regions from two…

Q: of the function. + 3y + 11

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Q: Find the linear approximation of f(x) = Vx-1 approximate 2.02. near a = 2. Use the result to

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Q: Find the absolute maxima and minima of the function f(x, y) = x² + y² on the closed triangular plate…

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Q: 1. Plot the function f(t) = (x+5) %3D 4+3x2 for -35 x 5.

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Q: Find the absolute maxima and minima of the function f(x,y)= 2x^2-4x+y^2-4y+1 on the closed…

A: See the explanation below

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: Find the (x, y) co-ordinates of the two stationary points of the function f(x, y) 3x2 + 6xy +2y³ +…

A: Given-  f (x, y)  =  3x² + 6xy + 2y³ + 12x - 24y So,

Q: Consider the function y= g(I)= -z² + 3c + 6,

A: The derivative of the function f(x) with respect to x is given as .

Q: The antiderivative of the function f(2) +7z is

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Q: Q3: Find fxx of the function f (x, y, z) = -In/1-x2 - y2 – z2 %3D

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Q: Q4) f(x, y) = x'/3 – x/ay² is harmonic ? Does the function

A: our objective is to conclude result.

Q: Find the largest domain (in R²) for the function 1+ Vx + Vy x² + y? f(x, y) =

A: The domain are those values of x,y; such that f(x,y) is well defined. Well defined means that the…

Q: Consider the function f(x, y) = 4x² – 8y² subject to the condition x + y = 25.

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Q: Find the maximum or minimum value of the function. f(s) = s2 - 1.2s + 16

A: f(s)=s2-1.2s+16Formula for the equation isf(x)=ax2+bx+cx=-b2aSo, s=-(-1.2)2  =0.6

Q: Find the local extremum of the function • f(x,y) = xy² – 6x² – 3y²

A: Find the local extremum of the function f(x,y) = xy2 - 6x2 - 3y2