How is derivatives utilized in solving for the dimensions and total area of a box?

Q: How is linear approximation used to approximate the value of afunction ƒ near a point at which ƒ and…

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Q: What is the shape of a graph in application of derivatives?

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: Find the approximate volume of a spherical shell whose linear radius is 3 inches and whose thickness…

A: Find your answer below

Q: y = x*lnx %3D %3D

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Q: What are the the mean value theorem in application of derivatives?

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Q: Sketch the x^2 And the derivative And integration

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Q: ind y' by implicit differentiation: xy3 - sqrt (x2 +1)=2y

A: Definition used -    Implicit differentiation-  If equations do not define explicitly y as a…

Q: x)= xーン %3D

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Q: Explain the derivatives and integration.

A: Solution: Derivatives: Definition of derivatives is , the rate of change of a quantity with respect…

Q: 6. A rancher wants to fence off a rectangular corral with an area of 4050 sq. yds next to a river.…

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Q: Find the partial derivative. 17zy

A: Given, ∂xe17xy∂x We have to find the partial derivative.

Q: Find the derivative of the function. %3D y = /x(x – 3)² y' =

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Q: Use implicit differentiation to find and %3D 2y %3D

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Q: What are the maximum and minimum values in application of derivatives?

A: We have to define the maximum and minimum values in application of derivatives.

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: How can you relate antiderivatives as an opposite of derivatives in your life? explain

A: Solution is given below:

Q: Calculate the derivative.

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Q: How can linear approximation be used to approximate the changein y = f(x) given a change in x?

A: Given;                 y=fx How can linear approximation be used to approximate the changein y=f(x)…

Q: Explain how to determine Partial derivatives for y-value ?

A: For a multi variable functions like f(x,y) To find its partial derivative for y value, treat x as a…

Q: One boat is 20 nautical miles due North of point A traveling toward point A at a rate of 15 nautical…

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Q: Find the derivative. y = ecosh(8x) y'(x) =

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Q: Use differentiation rules to find y' = dy/dx.

A: To determine the derivative of the function.

Q: Differentiate by using implicit differentiation x2y+xy2=6

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Q: How can the derivative function definition be applied to this problem?

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Q: 1. у %3D 4x2 — 3х — 2.

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Q: Find the derivative of y = x. %3D

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Q: Use the linear approximation to estimate

A: In this question, by using a linear approximation to evaluate the value of the expression using…

Q: How can you relate antiderivatives as an opposite of derivatives in your life?

A: Solution:   Antiderivatives are the inverse operations of derivatives or the backward operation…

Q: Draw the function x = 2y- y2 by using the tools of derivatives? %3D

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Q: Without doing partial derivatives, use your knowledge of trig function graphs to describe the shape…

A: The derivative is defined as the rate of change of one quantity with respect to another. In order to…

Q: Find the derivative of the function: (DO NOT SIMPLIFY): 2z f(z)%3D +2 (高)

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Q: What is the derivative of y = ekx?

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Q: Explain graphically: The endpoint approximations are less accurate when f , (x) is large.

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Q: As an application of partial derivative of multi-variable functions, provide one page about Lagrange…

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Q: What is the first-order derivative of y = x^y?

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Q: Find the derivative of the function. Vs - 3 f(s) = Vs +3 %3D

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Q: Explain how to determine Partial derivatives for x-value ?

A: Partial derivatives :- Let z=fx,y be function of two independent variables x and y. If we keep y  as…

Q: ential equation is given by

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Q: Find the derivative of the function. y = x²V25 - x² %3D %3D

A: Differentiate wrt x

Q: Find the derivative of fx Fx=8x3 cot x

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Q: How does the partial derivative relate to the limit of a function of two variables?

A: Solution

Q: Find a result by using variable separation for ý=secy b- xý = x + y

A: As per our guidelines we only solve one question and rest of the question will be reposted.

Q: A gutter is to be made from a piece of sheet metal that is a inches wide by bending up pieces of…

A: Width of the metal sheet = a inches We bend up x inchs on both sides.  So width of the gutter is =…

Q: Describe how you would use the second derivative to determine a local minimum or maximum.

A: Given data is: How you would use the second derivative to determine a local minimum or maximum

Q: Find the partial derivative. Find fx(3, -7) when f(x,y) = 7x2-9xy. O -21 O -126 O 21 O 105

A: differrntiate partially with respect to x

Q: Explain whether the Quotient Rule should be used to find the partial derivative

A: Partial Differentiation:     ∂∂x(xyx2+1)ddx(uv)=v.dudx-u.dvdxv2

Q: Find the derivative of f(x) : %3D

A: We need to differentiate the function f(x)=1x with respect to x. We also know that ddxxn=nxn-1.

Q: Find y" by implicit differentiation. 9x2 + y2 = 4 y" = %3D

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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.