Given the functions f (x) = Vx – 1 and g(x) = x² + 7: a. Calculate f(16) and g(3). b. Write f(16) as an ordered pair. c.. Write g(3) as an ordered pair.

Q: Given the Cobb-Douglas function f(x, y) = 30x0.3y0.7, x is the number of units of capital input and…

A: Marginal productivity of capital at x=4500 and y=3000 is:

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A: This is a Fourier analysis question. Lets solve it.

Q: Does the function y = e-3t satisfy the following differe y" + y' + 12y = 0

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Q: The function y=f(x) satisfies the conditions y(0) = 1 and y'=xy³/4. What is y(1)?

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Q: Find y as a function of t if 9y" +12y + 29y = 0,

A: 9y''+12y'+29y=0which condition y(2)=8, y'(2)=9To Find: y(t)

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

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Q: For the function f(x.y) = e 4xy, find f, and f,. f, =

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Q: Differentiate the function with respect to y. A Z = + Bey уб Z' + Bey = 8A 9 y 20 -

A: In this question we have to differentiate the function with respect to y.

Q: Find the image of the function f(x.y) = 36 + 1\4 v(9x² + 4y³)

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

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Q: Determine and distinguish the stationary values of the function f(x, y} = x² – 6x² – 8y². -

A: We need to find the stationary value of f(x,y)=x3-6x2-8y2   For that first we need to find the value…

Q: 2 (d) T (x) = Væ + 9Væ7

A: T(x)=x+9x73-2x25Formulaamn=amn1at=a-tddxx=n xn-1

Q: What is the domain of the function f(x, y) = x² /ỹ – In(x)?

A: topic -  function domain and range

Q: Examine the function f(x, y) =-3x-4y+15x - 16y + 6 for relative extrema.

A: Here we have to find relative maximum.  The solution is in both 1st and second steps.

Q: Find the domain of the function f(x, y) : Vx2 + 8y2 – 5.

A: follow next step

Q: For the function f(x,y) = 8x² + 7y², find f(x + h,y)-f(x,y) = h f(x + h,y)-f(x,y) h

A: Given, f(x,y)=8x2+7y2

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

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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: For the function f(x.y.z)= 3+5xy"-2z*, find f,, f, and f. -口 fx = 5-口 fy=

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Q: For the function f(x,y) = 7x² + 6y², find f(x + h,y)-f(x,y) = h f(x+h,y)-f(x,y) h

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Q: For the function f(x,.y,2) In (8x2 -7y4 +2xz2), find f, fy, fz, and fz

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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: Find the function U, whose first difference is *C,-

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

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Q: If f(y) = V4 - 7y, find f'(y). Use exact values.

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Q: Find dz implicitly of the relation r + y³ = 3ry.

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

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

Q: Calculate the point where the functions h(x)=3−3⋅x2 and w(x)=3⋅x+4 intercept. A.) Give its…

A: Topic:- algebra

Q: The productivity of a manufacturing company is given approximately by the function f(x, y) = 20x…

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Q: Differentiate the function. f(t) = 7 - 글

A: We have to differentiate of the  function

Q: Given the function f(x) = 3 %3D when it could be discrete

A: Given f(x)= 3x+7 Now we write a real world problem for the given function In the given function , 7…

Q: The derivative of the function y = 7x² + 12 – is: - 15 a) y' = 14x + x2 15 %3D b) y' = 14x + %3D c)…

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Q: From now on consider the function f(x, y) = e$n(x) y.

A: direction of fastest increase is along the gradient vector  Given f(x,y)=esinx y

Q: The function f(x, y) : 1+2? +y? is 1-x2 -y? discontinuous at the points {(x, y)\æ² + y² # 1}. True…

A: The given function is f(x,y)=1+x2+y21-x2-y2

Q: For the two functions f (x, y) = x³ – 3xy² and g(x,y) = 3x²y – y³ %3D Which one of the following…

A: The solution for the above question is as shown below.

Q: For the function f(x,y) = 5x² + 6y², find f(x + h,y)-f(x,y) h 11 f(x + h,y)-f(x,y) h

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Q: f (x) = x 2 satisfies the Horizontal Line Test on the domain {x : x > O}.

A: Horizontal line test is a test used to find the function is injective that is one-to-one. First…

Q: Find f, for the function f (x, y) = yx-2z'y %3D

A: we have to partially derivative

Q: Consider the following function: f(x, y) = 7x°y³ + 6x³y$ + 16 Step 3 of 3: Find fxy.

A: Given function is  fx,y=7x5y3+6x3y5+16 differentiating this with respect to x,…

Q: a. by using the appropriate Chain Rule and b. by converting w to a function of t before…

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Q: of the function. + 3y + 11

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Q: f(x) = 6x5 – 4x3 + 10

A: To classify the stationary points of the function: f(x)=6x5-4x3+10

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: For the function f (x, y) = /(x – 1)2 + y2 + 1

A:

Q: The domain of the function f(x, y) = 3x + xy + 5y? is R.

A: We have to verify that the domain of the function fx,y=3x+xy+5y2 is R or not.

Q: (b) Find the Linearization of the function: f(x)= Vx at a= 27 and use it to approximate the number…

A: Let the function is f(x)=x3 Let a = 27   Formula: Linearization of the function f(x) at x = a…

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

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Q: 19. Given the following functions: y = 8x – x2 and y = 3x %3D | Find their points of intersection.

A: SINCE YOU HAVE ASKED MULTIPLE QUESTIONS IN SINGLE REQUEST, WE WILL BE ANSWERING ONLY THE FIRST…

Q: g (x) = (/9x + 3 ) (7x² + 1)

A: Find your answer bellow

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.