2x + 1 , x < 3 i ci x 2 3 If the function g(x) = %3D x - 1 a) - 6 b) 6 c) 4

Q: 3. If dt , find g'(2). 5. g(x) =

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Q: then fxy Q4: If f (x, y,z) = x²y³ – y²z3 %3D -

A: we have to find partial derivative

Q: The productivity of a country is given by ​f(x,y)=14.41x0.427y0.573​, where x is the amount of…

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Q: 2. F(x, у) %3D — (у i-2x) y2

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: (a) 3 Differentiate y= y 3= us ing first principle. 2x+2

A: we are allow to do one question at a time  if you rest of answere please specify that part and…

Q: To the reci max z Ax1 +B x2 A=6 s.t. 2x +4x 2 12, B=1 -X1 + 2x2 S 2, X1 20, x2 Free.

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Q: = x² – 6x + 13, y = Inx, x = 1 ve x = 5

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Q: a) f„(x, y) b) f (х, у) уу ух 1 3 Зу'х + 5ху 3y'x .3. f (x, у) 16x*y4 -

A: (a)

Q: Solve the dff oq 2. 3. 3. %3D 1

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Q: 4.3 Verify that for f(x, y) = 4x°y$ - 9x*y³. дх ду ду дх df

A: Explanation of the answer is as follows

Q: y = xe * satisfies the equation ry' = (1 – x²) y. %3D

A: Given differential equation  xy'=1-x2y

Q: Solve Ytt = = 4yxx 0 0 Yx(0, t) = 0, Yx(1, t) = 0, Y (x, 0) = 0, y(x, 0) = 3cos(2nx)

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Q: Find the number in the interval [ – 1, - 0.25] so that the sum of that number and its square is…

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Q: Solve for the domain and range of. f(x,y,z) = %3D V4-x2-y²

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Q: I have equation 3x(y-x)=0. Is it true that x here is equal to 0 and y is equal to x? How can I show…

A: To check:  Whether x here is equal to 0 and y is equal to x. Given information: The equation is…

Q: Find all values of x satisfying the given conditions. y1 = 11x- 5, y = 4x +4, and y, exceeds y, by…

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Q: Solve 2sinx- V3 = 0 on interval [0,2 t)

A: We have to solve  2sinx - √3 = 0 on interval [0 , 2π)  Since ,  2sinx - √3 = 0  2sinx = √3

Q: Find the point on the graph of y = 1x that is closest to the point (2, 0). [Hint: 2(x - 2)2 + y2 has…

A: Given: y=x Let the point closest to (2,0) be P(x,y). Distance between point P(x,y) and (2,0) is:…

Q: Find fx (x,y) and  fy (x,y).  Then find fx (2, -1) and fy(-4,3)

A: Given: f(x,y)=ln|3x4+5x2y2|∂f∂x|(2,−1)=fx(2,−1)=?∂f∂y|(−4,3)=fy(−4,3)=?

Q: Find two positive numbers x and y that maximize Q = x2y if x + y = 2.

A: Given function - Q = x2y               ...........(1)And,x+y = 2y = 2-x…

Q: Solve for A y and dy if y = f (x) = -3x + 2x2 – 3x +5 %3D and

A: Given that: y=f(x)  =-3x3+2x2-3x+5

Q: Maximize f = 5¤1 + 7x2 + 11a3 subject to 10r1 + 8x2 + 11a3 0

A: Consider the provided LPP problem, maximize  f=5x1+7x2+11x3Subjected…

Q: x^2=Axy+By

A: Simple value put

Q: A consultant advises the owners of a beauty salon that their profit p each month can be modeled by…

A: The profit p(x)=-50x2+3500x-2500

Q: Find yll of x³+y²=3 by implicit ditferetlal C1o pants

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Q: 2 The Range (Ry) of y = v9 – x² -

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Q: Evaluate the Cauchy principal value of 2x² - 1 fo dx. x4 + 5x² + 4

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Q: II. Verify that ду дх дх ду 3 2 2. f(x, у) %3Dх'у? — ху 'y² – xy ³

A: Given function: Now,

Q: *宗+> B. If z = show that x 3z %3D x+y

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Q: What is the counterexample of x/x=1

A: Follow the steps.

Q: What is the particular solution for y′=−6x+3 that passes through the point (−4,−8)? Do not include…

A: The given differential equations is y′=−6x+3.

Q: A farmer wishers to fence off three identical adjoining rectangular pens, each with 300 square feet…

A: Given, Cost of the fence of outer boundary of the pens = $3 per foot Cost of the fence of two…

Q: Q2) Show that y = 35 x* – 30 x2 +3 satisfies ( 1- x² )y" – 2xy' + 20y = 0 %3D

A: y =35x4 - 30x2 +3 satisfy (1-x2)y" - 2xy' +20y =0 for this wew find  y" and y' y' = 140x3 - 60x y" =…

Q: Verify that 0t ду дх дх ду 2. 3 y 3 f (x, у) %3D 2х*у — х"у — ху

A:

Q: e 60x1 + 70x2 Subject to: 2x1 + x2

A: Given,   Maximize           60x1+70x2Subject to coinstraint:            2x1+x2≤300…

Q: What value of c will satisfy y(x) = c(1 – x²) given y(2) = 1 ? %3D ) Option 1 Option 2 2.

A:

Q: Minimize F = 24x2 + 24y2 with xy2 = 16.

A: Minimize F = 24x2 + 24y2 with xy2 = 16.

Q: 11. Perpendicular to 5y = 2x – 6 and passes through the point (-1, 5)

A: Given, The line is perpendicular to 5y=2x-6 and It is passing through the point (-1, 5). Concept…

Q: Suppose z – 2z +x=5, What is the value of y ?

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Q: 11 sec²(3t), 0 < t C₁ and C₂ as arbitrar

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Q: -2 The domain of f(x,y) = is %3D x² + y?

A: f(x,y)=-2x2+y2

Q: Find fx(x,y) and fy(x.y). Then, find fx(- 4, – 1) and fy(- 1,3). 23| f(x.y) = In |8 + 5x²y³|

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Q: 8 If f(x) dx = 37 and g(x) dx = 12, find %3D [2f(x) + 4g(x)] dx.

A: Given ∫08f(x)dx=37 and ∫08g(x)dx=12We have to find ∫08(2f(x)+4g(x))dx

Q: f (x, y) x+ 3 ху 3 Бъ-х

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Q: Use the characteristics method to solve the problem U, +3yU, = 2U , U(x,1) = f(1+ x,)

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Q: ax+b 35. у%3D cx+d 36. y= (x'+4x) 1) 37. y (r-x+ 38. y = V1+2x+x 39. y= (1+x*)" (1 +x* 40. у%3 (r*…

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Q: Z=Xi tXz – 2X3 Min Sito X, 4 YXq - Xg =do 2X, +3X2+X > 20 760 Xガフ0jーム2,3 Using M-tech i Lue

A: Min Z=x1+x2-2x3 subject to x1+4x2-x3=10                 2x1+3x2+x3≥20                 3x1+x2+4x3≥60…

Q: ,2,,2 Suppose that f(x, y) = 10x²y² + 6x? + 2y? then find the discriminant of f.

A: We have to find the discriminant from the given function

Q: Suppose x and y are positive integers such that the sum of x^2 and y is 10x. Find the values of x…

A: Given x^2+y=10x.From there find y.