For the given function f(x) = cosx, let xo = 0, %3D X1 = 0.5, and x2 = 0.7. Find the value of lagrange coefficient L2(x) of degree 2 at x = 0.75.

Q: Find by implicit differentiation. (Exercises from the text are numbered to match) a) #8 x³ – xy? +…

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Q: a) Find the differential dy, and b) evaluate dy for the given values of x and dx. y = e*/10 x = 0,…

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Q: Given that arcsec e) + (x – y²)² = 2. (a) Find dy using implicit differentiation. dx dy using…

A: Given,            arcsecyx+x2-y232=2

Q: Find the antiderivative of f(x) = sin^2x

A: Antiderivative=∫sin2xdxsin2x=1−cos2x2So,∫sin2xdx=∫1−cos2x2dx=12∫1−cos2xdx=12∫1dx−∫cos2xdx=12x−∫cos2x…

Q: Find the differential dy of the given function. (Use "dx" for dx.) dy =

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Q: Find the value of dz and dz/ dy at the point A when x changes by (0.01) and y changes by (- 0.01) xe…

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Q: Given that y is a function of x defined implicitly by the equation: siny = 4x + xy Find the first…

A: Given that y is a function of x defined implicitly by the equation  siny=4x+xy

Q: Find the differential of the given functions. a) f(x) = sin(cos(22)) CoS %3D 2x b) g(x) x3 – 7x

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Q: The graph of x3 + y3 = 9xy is the folium of Descartes. Find dy/dx by implicit differentiation.

A: x3+y3=9xy

Q: 2. Integrate numerically the given function, fx0.1(1.2-x)(1-e20(x-1)) dx with the multiple-segment…

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Q: Find the differential dy of the given function. (Use "dx" for dx.) y = x/9 – x²

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Q: Given yz + x? z3 = e"y². Use implicit dz differentiation to find

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Q: Given e^x - x^2 + y^3 = xy, find dx / dy using implicit differentiation

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Q: Given = y² dx - and y(1) = 1. Let h=0.2 Find an approximated value of “y" corresponding to x=1.6,…

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Q: If y = f(x) is the solution of (-x – 9)dx + (x2 + 10x + 41)dy = 0, f(0) = }In(41) +arctan(5/4), then

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Q: cinxo ) 2X. dy dx Find for y= cos ( Inx + e

A: We have to find the derivative.

Q: The displacement of a structure is defined by the following equation for a damped oscillation: y=9e…

A: The displacement of a structure is defined by the equation  y=9e-0.7tcos4t…

Q: dy = ( e )dx

A: See the attachment

Q: Find the differential dy of the given function. (Use "dx" for dx.) y = x+3/2x-3

A: Quotient rule of differentiation:

Q: Calculate the error of approximation with EA for the following functions TC f(x = 4 cos 5x when x =…

A: We know: lim∆x→0∆y∆x = dydx…

Q: Find for the following function: dx 1- y = sin-1 2x + 3

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Q: Solve using the integrating factors by inspection (y²-3-x) dy + ydx =0

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Q: Given that y is a function of x defined implicitly by the equation: siny = 4x + xy Find the first…

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Q: Find the differential dy of the given function. (Use "dx" for dx.) 6. y = 2/x +

A: Given:

Q: Given a function ƒ that is differentiable on its domain, write andexplain the relationship between…

A: The differentiable function is f on the interval I which contains a point a. The linear…

Q: 3. x cos x dx

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Q: when

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Q: Find the antiderivative of f(x)=cos(3x)

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Q: of

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Q: Obtain the general solution using variation of parameters (D²+3D+2)y=cos(e^-x)

A: We have to solve the given differential equation by variation of parame

Q: Find the differential dy of the given functions . (Use "dx" for dx.) a) y = 2x − (sin(x))2 b)…

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Q: Find the value of dz and dz/ dy at the point A when x changes by (0.01) and y changes by (-0.01) xe…

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Q: Given x +2xy– y² +x= 2. Find dy at (1,2) using implicit differentiation. dx

A: We need to use simple  differenciation

Q: If y = 1+ sin t ,x = cost at t == 2 Find- dt by using Chain Rule, then choose the correct answer:

A:

Q: The displacement of a structure is defined by the following equation for a damped oscillation: y=9e…

A: Displacement Of A Structure Is Defined By The Following Equation For A Damped Oscillation: y = 9e^…

Q: Find the differential dy of the given function. y = √x +1/√x

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Q: Find the differential dy for y = x2 - 4x + 6, then evaluate it when x = 2 and dx = 0.1

A: Differentiate the given curve y=x2-4x+6 w.r.t.  x use the power rule of differentiation i.e.…

Q: Use Taylor's formula at the origin to get a cubic approximation of the function: f(x,y) = ln(2x + y…

A: Given function f(x,y)=ln(2x+y+1) and a,b=0,0 Taylor's expansion  at origina,b=0,0 to get a cubic…

Q: Given y = 4e* + In x, find the differential dy. %3D

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Q: consider your implicit function. e^y=sin(7x). Dtermine the formula for dy/dx in terms of x.

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Q: #@3 g (x1y) =- 7x3 -49xy + 7y3 Find and elassify all the extrema of the fine tion

A: Given- gx,y=7x3-49xy+7y3 To Find- All the extrema of the above function. Concept Used- Using the…

Q: Find the differential dy of the given function. (Use "dx" for dx.) x + 1 4x - 7 dy

A:

Q: 3. Given x?y? = x² + y², find by implicit differentiation. dx

A: To find: The value of dydx. Given: The equation is x2y2=x2+y2. Formula used: Product rule of…

Q: Find the differential dy of the given function. (LUse "cx" for dx.) x +3 3x

A: We will solve the problem

Q: Find the antiderivative of the function f(x) = - 4 sin (4x) when C = 0. The antiderivative is

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Q: xy = In (2y) – e

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Q: Find for the following function: dx 1- y = sin-1 V2x + 3

A: See the attachment

Q: Find the differential dy of the given function. (Use "dx" for dx.) y = arctan(x – 2) dy = ||

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Q: Find the antiderivatives |x In(x²) dx + sec? x dx CO X dx sin5

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Q: In the given DE, cos x + In y + ( + ev = 0, integrating the coefficient of dx, M (x, y), with…

A: We will find the g(y) as shown below

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.