Find the image of the line y =-x under the mapping = f(z) =2² + 4z %3D %3D

Q: Find the gradient of the function f(x,y) = 4y - 9x at the point (9,3). Then sketch the gradient and…

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Q: Find the point on the planez = x + y + 1closest to the point P = (1, 0, 0). Hint: Minimize the…

A: Let Q(x,y,z) be the point closest to the point P. Let D be the distance between these two points.…

Q: Find the minimum distance from the point to the plane x-y+z=3 at (1,-3,2)

A: We will find the minimum distance from the point to the plane x-y+z=3 at (1,-3,2) in the following…

Q: Find the between the two curves. area 2. X=ay, a'y=x 3

A: The area between the curves can be calculated by integration. The formula used for the integration…

Q: 4xy* :- find f,,f, at point (4,1) for f(x,y) = x’e**Y

A: I have used partial differentiation

Q: Let y= 3x2 +7x+4. If Δx=0.4 at x=2, use linear approximation to estimate ΔyΔy

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Q: Illustrate local linearity for the function f (x) = xsinx at x = l.

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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: Find the aren of the region in the tirst quadrant baunded by the line y=27, e the line X-4, the…

A: We first sketch the region using a graphing calculator.

Q: Find y' for y = vTy at the point (9,1).

A: Given: y=xy ⇒y=x12y12 ⇒y12=x12

Q: Classify all level curves of f(x, y) = Vy² – x² and draw its contour map.

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Q: What is the largest vertical distance between the graphs of the functions y = Va and y x2 in the…

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Q: Find the local minimum value of f(x, y) = 4 + a" + yl – 11ry.

A: Use double derivatives test to find local maximum or minima.

Q: What is the maximum slope of f(x,y,z)=yex-x2sin(z) at the point (0,7,5)?

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Q: Find the centroids of the function, y=4x-x^2, y=x (please sketch the graph)

A: Let's find.

Q: find the point on the line y=2x+10 that is closest to the orgin, (0,0) What is the minimum distance?

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Q: Find the absolute maximum and minimum of the function f (x , y) =x² + y² on a closed triangular…

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Q: What is the maximum slope of f(x,y,z)=ye^x-x^2sin(z) at the point (0,7,-3)?

A: Given the function fx,y,z=yex-x2sinz and the point 0,7,-3. Computing the partial derivatives,…

Q: Find all points of horizontal and vertical tangency to the curve: x = 3cos 0 y = 3sine

A: for Horizontal tangent put dydθ=0 for the vertical tangent put dxdθ=0

Q: What is the maximum vertical distance between the line y = x + 2 and the parabola y = x2 for −1 ≤ x…

A: Consider the given line

Q: What is the ALGEBRAIC RULE for REFLECTION over the line y = x? (х, у) —

A: This question is related to reflection of coordinates, We will solve it using given information.

Q: Find the center of mass of the thin plate bounded by the y-axis and the lines y =x and y = 2 - x…

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Q: find the gradient of function f [x, y,z] = 3x² -y?_z? at paint {i,-Ź, -¡}

A: The given function is fx,y,z=3x2-y3-z2 and the given point is 1,-2,-1. The gradient of the function…

Q: What is the largest vertical distance between the graphs of the functions y = v and y = x in the…

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Q: Find the linearization of f(x, y) = −x² + 2y² at the point (3,-1). Use the linearization to estimate…

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Q: Find the are length of the curve 2x = 3 y over the interval from y=0 to y=1

A: To find: The arc length of the curve in the interval . Formula used: The arc length of the curve…

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

Q: Find the minimum values of the function (x, y) = x² + 2y² that lic on the cirele x² + y² =1

A: Given : Function fx,y = x2 + 2y2  Circle x2 + y2 = 1   To find : Minimum values of the given…

Q: Sketch the region in the xy  -plane defined by the equation or inequalities. -1 <=y<=3

A: -1≤y≤3

Q: Find the absolute maximum and minimum of the function f(x,y) = 2x² - 4x + y² - 4y +6 on the closed…

A: Given that a function f( x , y ) =2x2-4x+y2-4y+6  on the closed triangular plate bounded by the…

Q: Find the slope of the surface z = f (x, y) in the y-direction at the point (64, 8).

A: Follow the procedure given below.

Q: The slope of the surface z = xy² in the x- direction at the point (2, 3) is O 12 O 8 O 1 O 9 O 10

A: The slope of the surface z = f(x,y) in the x-direction at (x0,y0) is given by [∂z/∂x](x0,y0) =…

Q: Find the absolute maximum and minimum values of the function on the triangular region whose vertices…

A: The given function f(x, y) is a polynomial and therefore, it is continuous and has both maximum and…

Q: Plot the function f(x, y) = x² – y² over the square region bounded by the lines y =x - 2, y =x+ 2, y…

A: Given the function fx,y=x2-y2

Q: Calculate the gradient. 5x g(x, y) = x² + y? (Use symbolic notation and fractions where needed. Give…

A: first calculate the gradient for partial differentiation.

Q: Find the points on the graph of the function f(x) = x^2 that are closest to (0, 2) in the xy-plane.…

A: Minimal distance

Q: Find the maximum and minimum value of f (x,y) =x' + 3xy² – 3x² – 3y² +4 = X" - -

A:

Q: The slope of the secant line of the function y =Vx +x through the points x, = 1 and the point xz = 4…

A: y=x+x

Q: hich vect וdtiolו y and 2? 1 -2 y = 1 -6 x = 2 8 -1 2 -1 5 2 -3 [ 2 -1

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Q: Find the absolute maximum and minimum of the function f(x,y) = 2x - 8x + y - 8y + 2 on the closed…

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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: C(x) = 1500 + 13x – 0.1x2 + 0.0005x3. - %3D Find the marginal inal cost finctien?

A: Given query is to find the marginal cost function.

Q: Find a curve in the xy-plane passing through the origin andwhose slope at the point (x, y) is x + y.

A: we have to find a curve in the xy-plane passing through the origin and whose slope at the point (x,…

Q: Find the distance between the plane x+y +z = 3 and the line L= λ(1,0,-1).

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Q: Find the point where the minimum value of f(x, y) = xy subject to y = 90 – x occurs.

A: Find the point where the function f(x,y)=xy subject to y=90-x2 attains its minimum value.

Q: Integrate the function f(x, y) = x – y over the triangle T with vertices (0,0), (1,0), and (1, 2).

A: Evaluate : ∫∫T(x-y)dA        ......(1) ∫∫Tx-ydydx T is the region enclosed by the triangle. Region…

Q: Find the absolute maximum and minimum values of f(x, y) = x^2 +xy + y^2 - 3x + 3y on the triangular…

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Q: Use Lagrange multipliers to find the minimum distance from the curve or surface Line: x − y = 4 to…

A: To Find: Use Lagrange multipliers to find the minimum distance from the curve or surfaceLine : x-y=4…

Q: I Sdve for dydx using the four-step rule 2. Y = x- x 2.

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Q: What is the largest vertical distance between the graphs of the functions y = Vx and y = x² in the…

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Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.