Find the critical point of the function f(x,y) = 4x²y² + 3y2 + 5x2. %3D o a. (-0.87,0) o b. (0,-1.12) o c. (0.87,0) o d. (0,1.12)

Q: Let f(z, y) = zy-y+a?. D.((1,2) =? where u=. OA- O B. -37 Oc- 37 OD.

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Q: Identify the removable discontinuity. x2 – 16 f(x) : X – 4 (x, y) =

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Q: Show that the function u(z, t) : satisfies ua = %3D %3D a2t2-2

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Q: Given a function f(x,y,z) = 8x2 In (5y + 9z). Find the domain of the function. o {(xy.z) | z>1-…

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Q: Find F′(x).

A: We know that, ddx1x=-1x2 Also, ddxaf(x)=addx(f(x)) where a is a constant.

Q: x' +4x? + x - 6 f(x) =マ+x-4x -4 %3D X' + X 4х

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Q: 23. Let f(x) = 3x - 1 and g(x) = x – 2. (a) If f(2x) =g(3x), find the value of x. (b) If H(x) =…

A: Given:fx=3x-1gx=x-2 To find: (a)   If f2x=g3x, find the value of x (b)   If Hx=3fx+2gx and Ha=5,…

Q: Evaluate : dx O X+4

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Q: Find an expression for dy/dx. y= (u+5)(u-5) u= x2  + 7

A: Given expression are  y=u+5u-5=u2-52                                Using a+ba-b=a2-b2=u2-25…

Q: 2. If w = f(x + ct) + g(x- ct) show that c²wxx = Wtt C= constant.

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Q: Differentiate the function. 6. 2. y = .2 x +1 Choose the correct setup below to differentiate the…

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Q: Could you help me solve and understand d-f?

A: d.The required value is calculated as follows:

Q: If V (r" F) = 0, find the value of n.

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Q: For f(x) = x? – 5x - 6, find f(2), f'(2), and f(3) – f(2). f(2) = a. b. f'(2) %3D c. f(3) – f(2) -

A: The given function is fx=x2-5x-6

Q: (b) Consider the non-stationary series {Xt}, Xt=t+St+ €t where St has period 2 and ~ iid(0, ²) and…

A: A non-stationary series Xt is given such that: Xt=t+St+εt where St has a period 2 and εt~iid0,σ2.

Q: 1. dy dt 2 3 14 S I = lim At→0 =lim At 0 = lim - At→0 = lim lim At→0 f(t+At)-f(t) At 2 -7. 2 +At At…

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

Q: 5 Given yz - Y1 = m(x2 – x1). Soive for x2- %3D

A: Given y2-y1=m(x2-x1)

Q: хр %3D S + X хр Find at (-7, 1) if xy: %3D (Rou

A: We have to find dy/dx   at (-7, 1)

Q: ots.) Let f (x) = and g(x)= 2x+3. X-3 %3D a. Find (fog)(x) b. Find (gof)(x) C. Are f and g inverse…

A: a) Plug g(x)=2x+3 inside f(x) and then simplify.

Q: Find f, (9,0) if f(x,y) = 4x eY. fy(9,0) = (Simplify your answer.) %3D

A: We can find the required answer as below

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A: Given:The function y2x2 = 1.The point (2,1/2).

Q: Q4: Find frr, fay, fyr and fy for f (x, y) = e*ly

A: We have to find double partial derivative of given function.

Q: d y Find dx? |(-1,2) if x² + y' = 9

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Q: f(-1,–5)= f(-5,–1)= f(0, 0)= f(5, –5)= f(t, 2t)= f(uu, и — v)-

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Q: Find the centroid of the plane area shown below using integration. y²= 3x - y = x²/3 -X

A: The centroid or geometric centre of a plane figure is the arithmetic mean position of all the points…

Q: Find the values of a and b such that a = b + [¹ f(x) dx − [*f(x) dx = f*f(x) dx. - 11

A: Given,