Find the marginal revenue function. R(x) = 7x – 0.05x² R'(x) =

Q: The tangent line to the graph of y=f(x)at the point (1,11) has the equation y=3x+8 (a) Find f′(1)…

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Q: Find the relative extrema using both First and Second Partial Derivative test f(x) = Sin2x ; 0<x<n

A: i) The given function is fx=sin2x. Given that the domain of the function is 0,π. Obtain the first…

Q: Evaluate.cuse C for the Constant of integration). 40 t6x-X dx

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Q: Find dy/dx by implicit differentiation. xy + 5x + 2x2 = 3

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Q: 5. Find of the parameters: x = sin 2t and y = - cost at t = dx %3D

A: Topic = Derivative

Q: x sec2x dx (integration by Parts)

A: In this question, we need to find the integral of given function using integration by parts.

Q: arctan x Xe fel Xaresecx d

A: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: Evaluate / x cos(128x)dx. Use capital C for your constant of integration.

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Q: OFind the second derivative of y = 4Vx + E + 10

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Q: 2. The rate at which the total average of COVID cases is dx increasing at x = 10 tents and 1 tent…

A: The solution are next step

Q: Find the cost function for the marginal cost function. 2 c'(x) = 3x - 10 units cost $288.95 X Write…

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Q: The integration of dx is 4+x²

A: The given integral ∫dx4+x2 can be evaluated as, ∫dx4+x2=∫dxx2+22                =12tan-1x2+C…

Q: find the partial derivative of the function with respectto each variable. ƒ(x, y) = 1/2 ln (x2 + y2)…

A: The given function is fx,y=12lnx2+y2+tan-1yx.

Q: Given a right circular cone with an altitude of 5 cm and a base diameter of 8 cm. If the diameter is…

A: volume of cone =Πr2h/3

Q: Find the most general antiderivative. dx x2

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Q: Find the length of the curve y =x2/8 − ln(x) on the interval [1, 2].

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Q: Find dy/dx by implicit differentiation. xy + 2x + 2x2 = 3

A: Given, xy + 2x + 2x2 = 3

Q: Find the linear approximation of f(x)=ln(x) x=1 and use it to estimate ln(1.1). L(x)= ln(1.1)=

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Q: 1. Find the rate of y with respect to x at the point (1,8) if 7y² - xy³ = 4. dy dx

A: Given: 7y2-xy3=4 and Px,y=1,8   As we know that; The Power Law: ddxxn=nxn-1 The Product rule:…

Q: a) The marginal profit for a product is modeled by dP -0.0002x + 14. 2 dx Apply the integration to…

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Q: Find the average rate of change of the function over the given interval. y =V4x + 1; between x 2 and…

A: To find the average rate of change of function y=4x+1 between x=2 and x=12

Q: 3. Find the equation of the normal line to the curve f(x) = 6e2* cos x at the point (0,6).

A: Given: fx=6e2xcosx; 0,6 We know that for finding equation of normal at given point, we need to find…

Q: /4 - x2 the integral | dx, becomes

A: Given the integrationI=∫4−x2x2dx

Q: 2 1 Estimate -dx using the right endpoint rule with n = 4 3 1+x

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Q: 7. Find the equation of a normal to y = x³ - 3x²+x-1 at x = 3

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Q: Find the nth-order differential of the function y=2x.

A: To find nth order differential of the given function.

Q: Determine the integrating factor xydy - (y2-3x2)dx = 0

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Q: Find dy/yx by implicit differentiation x^3-xy^2+y^2=2

A: Given function is x^3- xy^2 +y^2 = 2.Implicit differentiation is a special case of the chain rule…

Q: 5. Find where y = In(cosh(2x)) + /sinh-1(2x) + tanh² (7x). dy dx

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Q: Suppose that a company’s marginal revenue from the manufacture and sale of eggbeaters is dr/ dx = 2…

A: To determine the expected revenue from a production run.

Q: The average rate of change of the function y = x² in the interval 2 sx< 5 is %3D

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Q: 6) Calculate - dx for z = ln(x + y²).

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Q: Suppose that the revenue (in dollars) from the sale of a product is given by R = 60x + 0.9x? –…

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: Find the partial derivative. 4 = (x² + 6x – 3y)* - dz

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Q: The derivative of y= sech-1(x sechx)+e$inh (Inx) equals Select one: – x sechx tanhx+ sechx O y:…

A: Given

Q: Differentiate the following function.   y=ln(x+1)+ln7 dy/dx=?

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Q: Find2 of the parameters: x = sin 2t and y = - cost at t =

A: In this question, we need to find dydx. It is given that x = sin 2t and y = -cos t

Q: 3/ Find Value of integral ) dx 0 X+1

A: I am attaching image so that you understand each and every step.

Q: Find the linear approximation of f(x)=ln x at x=1 and use it to estimate ln(1.24). L(x)=?…

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Q: Find dy/dx by implicit differentiation. x7 + y4 = 5

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Q: Sx* (4 – x)* dx

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Q: A population x of rats satisfies the DE dx /dt ka?. Initially there are x(0) = 2 rats, and their…

A: The general solution of a differential equation always contains a constant of integration. The…

Q: Find the average rate of change of the function over the given interval. y = V4x + 1; between x =0…

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Q: Find the linear approximation of f(x)=lnx at x=1and use it to estimate ln⁡(1.3) L(x)=? ln 1.3≈?

A: First find the linear equation at x=1  then find the approximate values

Q: 1. If f(2) = 1, find the constant of integration for dx f(x) = +3

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Q: x e* dx

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Q: | (In x)2 dx Use integration by parts.

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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.