2. Sketch the graph of the function (a) f(x, y) = Vr² + y? (b) f(x, y) = Vx² + y? – 1 %3D

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Q: Find the linearization of the function f (x) = x' at x = 1. L (x) =

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Q: Compare the values of delta y and dy for the function f(x)= x^3 - 3 at x=3and delta x= 0.2

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Q: 2. dy sin x - y where f(n) = 0. %3D dx

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Q: 2. Show that the function u = p(xy) + Vry (y/x) provides the equation y². 0. dy?

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Q: Find the length of the curve /- y = Vcos 2t dt from x = 0 to x = "/4.

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Q: Suppose we have a revenue function given by R(z) = 6z- az?, %3D = 10? where a is a constant. What…

A: Given Rx=6x3-αx2 To find the value of α when average value is $20 for x=10

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Q: B)ls w = z²1² analytical function or not?

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Q: (1) Where on the line r = ay does the function f(x, y) = (x – a)² + (y – 2)2 attain its smallest…

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Q: Differentiate the function. y = 7x dy %3D

A: It is derivative problem.

Q: dy 2- Find for the following function: dx А- у%3Dх*. сosx B- y= 2(secx)²

A: Given : A) y = x3·cosxB) y = 2secx2

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A: Consider the cubic function: y=ax3+bx2+cx+d…

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A: Differentiate wrt x

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Q: Differentiate the function. y= (5x- 1) (1-x°) dy %3D dx

A: Given that the function is      y = (5x-1)2(1-x3)4

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Q: What is the linear approximation of the function f (x) = e x at x = 1?

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Q: Find the relative maximum and minimum values. f(x,y) = 3x² – 4y?

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Q: Find the maximum rate of change of the function f(x,y) =4x^2-2y^3 at the point (1,1)

A: Given data: The given function is f(x,y)=4x2-2y3. The given point is (a, b)=(1, 1). The expression…

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Q: 2. y = V4-x , x=0 and y=0 about the y- axis

A: Given that y=4-x2, x=0 and y=0 about the y-axis

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A: Given :           f(x) = (x + 2)5 at 0 To find :             The linear approximation of f(x)…

Q: What is the domain of the function w = ƒ(x, y, z) = 1/xyz?

A: What is the domain of the function w = ƒ(x, y, z) = 1/xyz?

Q: Find the linear approximation L(x) to y = f(x) near x = a for the function. f(x) L(x) =

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

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Q: Find the linearization of the function f (x) = x° at x =1. L (x) Using this linearlization, f…

A: To find the linearization of the following function

Q: Sketch the level curve of g(x,y) = y / 4 ln x corresponding to g(x,y) = -1/2

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Q: What is the value of dy/dx at x = 1 of the function * = (20" – a*) () x+1 y = - 2-1

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Q: Examine the function f (x, y) = x3 − 6xy + y3 for relative extrema and saddle points.

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Q: What is (V | and find the relative minimum dx point as indicated by the black dot on the graph at…

A: Here we have ;  y=xx ..................(1) taking log both of sides

Q: f(x, y) = 3xy – x²y- xy?

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Q: 4 + where f(1) = -2. y : dx 业

A: If (x, f(x)) is a point where f(x) reaches a relative maximum or minimum, and if the derivative of f…

Q: Sketch the graph of function f(x, v)- J4-x - and draw the level curves at k- 0, 1,4

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Q: What is the linear approximation for any generic linear function y=mx+b?

A: Given: y=mx+b

Q: Draw the level curves for the function z = f(x, y) given by z = /4 – x² – y² when z = 0, 1, 2 and…

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Q: Find dy/dx, where y is defined as a function of x implicitly by the equation below. x3+y4=3

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Q: Determine the length of the curve TC f(x) = In[sec(x)],0 < x < 4

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A: on doing partially differentiation with respect to x and y we get

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Q: Differentiate the function. y=[(sx +2x+3) (x-3)]² dy dx II

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Q: Find the slope of the graph of cos(x + y) = 2x at the point ( 0, T1/2 ). Hint: Differentiate…

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