This problem will have you determine an estimate of 1/V16.34 via a linear approximation. (a) What is the function f(x)? (b) What would be the point x = a to build the linear approximation around? (c) Determine a formula for the linear approximation L(x). (d) Compare the exact value of 1/V16.34 to the approximation found via L(x). Compute |approximation - exact| leхact the percent error in the approximation: 100 -

Q: ) Estimate the value of Csc (0. 2) using linear approximation and without using any kind of…

A: Given problem:- Estimate the value of csc(0.2) using linear approximation

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A: Given that the function is  f(x)= e-x, a= -0.1 To determine the linearization for the function.  The…

Q: 1. Find the orthogonal trajectories of the family of curves x? + y2 = cy.

A:

Q: 12)Estimate rio by using a linear approximation at aこ 9. timi

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Q: How can we minimize the error of an approximation in a linear approximation at the point (a. f (a))?…

A: Query- How can we minimise the error of an approximation in a linear approximation at the point…

Q: Find the orthogonal trajectories to the family of curves: x² = C-v'(ln y² –1).

A:

Q: 5/ Use the Newton - Raphson method to estimate the root of f(x) = e - x, employing an initial guess…

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Q: (1) Use the linear approximation of Va at x = 9 to estimate the value of v8.7

A: As per the guidelines, we are supposed to answer only one question at once. Kindly repost the other…

Q: 5. Deduce the standard linear approximation of 1 x2+y2+z2 at Po(1,2,3).

A: The general formula of the standard linear approximation for f(x,y,z) is generally given by,…

Q: i) Find the orthogonal trajectories of the family of curves: y : 1+ x?

A: By Bartleby policy I have to solve only first one as these 2 are unrelated problems

Q: find a linearization at a suitably chosen integernear a at which the given function and its…

A: Given, f(x)=1x, a=0.9 now find linearization f(0.9)=10.9=109 so linearization at 910,109…

Q: Compute the second derivative of  f(x)=ex+x  at x = 2 using a step size h = 0.2  The backward…

A: According to the question; f(x)=ex+x                                                     ; x=2step…

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Q: (6) Find the orthogonal trajectories of the 3C cos 0, where C family of curves r being parameter.

A: Answer

Q: Use Euler's Method with an appropriate h value of your choosing to estimate y(4) with y = 0.5, y (1)…

A: Topic- Differential Equation

Q: 8) Find the family Coff esponding to of orthogonal trajectories y=kx".

A: To find the orthogonal trajectories corresponding to below curve.

Q: Suppose X1, ..., Xn are iid with PDF f (x | 0) = 40ªx-5. x > 0, where 0 > 0. Find the method of…

A:

Q: (6)Find the orthogonal trajectories for the given families of curves 2x2 – 3y = K. Where K is a…

A: We have to find out the orthogonal families of given function Given function   2x2 -3y=K  ;    where…

Q: 4. Estimate the In (1.1) and sec (0.1) using a linear approximation and without using any kind of…

A:

Q: (6) Find the orthogonal trajectories of the family of curves r = 3C sin 0, where C being parameter.

A: Orthogonal trajectory curve of a family of curve is defined as a curve which intersects every member…

Q: .8 Estimate the error if cos t is approximated by 1 2 in the 4! integral cost? -- + - dt.

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Q: Find the orthogonal trajectories of the one parameter family of curves ex+e-y=c

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Q: Use differentials to approximate V36.1. 3.

A: Consider y = root x.Let take x = 36 and delta x = 0.1.Find delta y as follows.

Q: Use a linear approximation (or differentials) to estimate the given number. (1.999)3

A: First I have find the linearization of x^3 near x=2 and then find the required approximated value.…

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Q: A hollow cylinder has a radius R of the outer surface, radius r of the inner surface and height h.…

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Q: Use a linear approximation (or differentials) to estimate the given number. (8.09)2/3

A:

Q: Use a linear approximation (or differentials) to estimate the given number. (1.999)5

A: Given term is (1.999)5Let x = 1.999

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Q: What is the difference between the linearization, L(x), of f at a, and the linear approximation (or…

A: Given question:- What is the difference between the linearization, L(x), of f at a, and the linear…

Q: 1. Find a root of f(x)=x-e=0, using Secant method, correct to three decimal places use initial…

A:

Q: The

A: Below is sketch of  the given function.    Rotation about x axis will give a volume in 3D plane.

Q: Find the orthogonal trajectories to the family of curves: r=c- (in y -1).

A: Orthogonal trajectories can be find in the following way: (i) differentiate given family of curves,…

Q: 5. Find the orthogonal trajectories for a family of circles tangent to the at y-axis.

A: Here we have to find the orthogonal trajectories for a family of a circle tangent to the x-axis and…

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A: given  ∂2u∂x2=∂u∂t to find the finite difference approximation of the first derivative in the…

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Q: Use a linear approximation (or differentials) to  estimate the given number.  (1.999)4

A: Consider  1.9994

Q: 7) Use a tangent line approximation with the function g(x)= Jx to estimate V9.2

A:

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Q: Find the general solution to the DE using the method of Variation of Parameters: у" — Зу" + Зу' — у…

A: The solution is given as

Q: Estimate the In (1.1) and sec (0.1) Using a linear approximation and without using any kind of…

A: f(x)=ln(x) f'(x)=1/x f(1)=ln(1)=0 f'(1)=1/1=1 linear approximation is then L(x)=f(a)+(x-a)f'(a)…

Q: Consider the linear approximation 7 - x 7 A. Over what interval is the approximation accurate within…

A: 17-x≈x49+17To Find:a. The interval where the approximation accurate within 0.3.b. The interval where…

Q: 6) Find the orthogonal trajectories for the given families of curve 3x - y = c.

A: To find orthogonal trajectory first differentiate with respect to x then remove constant then put…

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A: Given function is,

Q: Let y = 5x² + 4x + 4. If Ax = 0.3 at x = 4, use linear approximation to estimate Ay Ay ~ Submit…

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Q: (6) Find the orthogonal trajectories of the family of curves r= 2C sin 0, where C being parameter.

A: See the detailed solution below.

Q: Find atleast three approximations of a solution of the equation f(x) = x – 2x = 0 by Newton Rampson…

A: Thanks for the question :)And your upvote will be really appreciable ;)

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.