Evaluate Exact error for Py (Y2) estimating f (Yz) where flx)= et, of degrée 4 atx=1) for fx)=ex Py(x) Tagler Polynomial

Q: Find the firct derivatioves of the follwing: - 3 ) y= 3x-x -2 4) y: Jerx 2) y: Ji-7x 5) y = 2メ-3

A: ddxxn=nxn-1 ddxu(x)v(x)=v(x)ddx(u(x))-u(x)ddx(v(x))v(x)2

Q: Use Taylor’s formula to find a quadratic approximation of ƒ(x, y) = ex sin y at the origin. Estimate…

A: The given function is,

Q: 2. Find the MacLaurin polynomial of degree 7 for the function F(x) So sin (6t²) dt.

A: SOLUTION-

Q: What is the maximum value of y = cos x. For - < x < < ?? 1 1/2 2.

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Q: Kim throws a ball against a wall at time t = 0. At time t = 1, it hits the wall and then at time t =…

A: The objective here is to check whether Mean Value Theorem can be applied to show that at some point…

Q: Show that f(x) = sin x (1 + cos x) is maximum when x = Hence find its maximum value.

A:

Q: Find the local linear approximation of f(x) at 4 + x xo = 3, where Ax = x – 3. NOTE: Enter the exact…

A: f(x)=14+x

Q: Use Taylor’s formula to find a quadratic approximation of ƒ(x, y) = cos x cos y at the origin.…

A:

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: 1. Find an estimate of the root of the equation: 3 = 5x2 located in the interval (0,1) using…

A: Note:  We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: Find the smallest positive root by using the bisection method Ax) = 2x-x with Residual error e<0.01

A: The given function is,f(x)=2x5-x3

Q: Find the length of the hyperbolic function y = cosh x from (0,1) to (8, cosh 8)

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Q: Perform error analysis of approximation derived (a) 1 x² 1 - at xo = 0 X (b) sin (₁) ₁ X- at x = = 0…

A: Given that: a 1x2-1 at x0=0b sin xx-1 at x=0c exp x2-1 at x=1 and x=-1 The objective is to analyse…

Q: 3G)Ú) Show that the reduction formula for atanx で-u sec"x dx = Sec" 「キu ) Hence use tthe formula to…

A:

Q: Suppose you want to prove that ARST Theorem. If you know that ZR = LX, what else do you need to…

A: In ∆RST  &amp;  ∆XYZ, ∠R≅∠X.

Q: Find the exact error in approximating ln(sec(−0.4))by its fourth degree Taylor polynomial at ?=0.

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Q: -4t Find the indefinite integral dt and verify the result by differentiation. (t2+3)3

A: Integrate using substitution than take derivative to verify the result.

Q: Use an appropiate linear approximation to estimate the value of In(1.01). Compare your approximation…

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Q: Find the linear approximation of the function at the given point. f(x, y) = 4 sinx - 6 cos y at (0,-

A: Given,           The function fx,y=4sinx-6cosy  at  0,π2.

Q: How does Taylor’s formula for a function ƒ(x, y) generate polyno-mial approximations and error…

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Q: Use Fourier cosine transform to solve y" – y = 3e-4 y' (0) = 0 lim y (x) = 0, as x → o0

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Q: Find the smallest positive root by using fixed- point method f (x) = In(3x)– x² +2 %3D with three…

A: Given: fx=ln3x-x2+2. We have to find the smallest positive root by using fixed-point method with…

Q: 4th degree polynomial of y=sinxcosx centered at x=pi

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Q: Use Newton's Method to approximate the zero(s) of the function f(x) = x' +4x +1

A: f(x) = x5 + 4x + 1 Basic formula for Newton's Method is: xn+1 = xn - fxnf'xn f'x = 5x4 + 41 + 0 =…

Q: What is the approximation of the value sin (1) obtained by using the fifth-degree Taylor polynomial…

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Q: 9) If f(x) = sinh() , then f'(x) = %3D (A) 3 cosh(÷)

A: Given: f(x)=sinh1x2To find:f'(x)

Q: Plot f (x) = ln x − 5 sin x on [0.1, 2] and approximate both the critical points and the extreme…

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Q: What is the isogonal trajectories family of curves x² - y² = a which intersects at an angle of ∅ =…

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Q: Find the linearization of ƒ(x) = √(1 + x) + sin x - 0.5 at x = 0.

A: substitute 0 for x in f(x)=1+x+sin x-0.5 to obtain the value of f(x) at x=0 f(x)=1+x+sin…

Q: Compute the point of intersection of the curve sinx and x-1 with the help of Bisection method. Ans.…

A: Disclaimer: Since you have asked multiple questions, we will solve the first question for you. If…

Q: Find a real root for x tan x+1 = 0 using Newton Raphson method.

A:

Q: Differentiate the Maclaurin polynomial of degree 4 for f(x) = ex . Describe the relationship between…

A: Maclaurin polynomial of degree 4 is P4x=f0+f'0x+f''02!x2+f'''03!x3+f404!x4.

Q: Estimate the slope f'(3.5) for f (x) = sin(3x) using: a. Forward difference approximation with h =…

A: f(x)= sin3x x y y1 y2 y3 y4 3.3 -0.1557             -0.193       3.5 -0.3507   0.0139…

Q: Consider f(x) = sin(2x) + cos(4x), 0 ≤ x ≤ 1 Construct a Langrange Interpolating polynomial of…

A: The given question is solved below

Q: By integration find the Fourier transform of Ax)=2r+1 _if þx|<1_and fx)=0 otherwise.

A: According to our company policy, I am supposed to answer only one question at a time. For the rest…

Q: Find the linear approximation for f(x)=sin2x at x=5π6 and use it to approximate sin2(147∘). Round…

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Q: Use forward, backward and centered difference approximations to estimate the first derivate of: tx)…

A:

Q: The 4th degree Taylor polynomial for sin(x) centered at a = is given by 6 V3 3 sin(x) = X - 48 +…

A: As per the company policy i can answer only first question for you, More than that leads me towards…

Q: Use Newton's Method to approximate the zero(s) of the function f(x) = x° +x+1 accurate to three…

A:

Q: The finite difference approximation of the first derivative in the simple implicit method used to…

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

Q: Find the absolute maximum and minimum values for f (x, y) = 4 sin(x) + 9 cos(y) on the rectangle R…

A: Given that: fx,y=4sinx+9cosy Limit: 0≤x≤2π, 0≤y≤2π We know that if a,b is a critical point and…

Q: 2. About what point is the local linear approximation l(x) 1 of the function f(x) = tan- x 4 valid?

A: Let's Solve,

Q: Find the linearization of ƒ(x) = sqrt(x + 1) + sin x at x = 0. How is it related to the individual…

A: To determine the linearization of the function at x=0.

Q: Find the local linear approximation of f(x) = tan¯(x – 4) at xo = 5, where Ax = x – 5. Enter the…

A: Given: fx=tan-1x-4

Q: Find a root of a equation f(x) = 2x³ - 2x - 5 Using secant bisection method when the initial…

A: Given : 2x3-2x-5=0Let  f(x)=2x3-2x-5

Q: B) Prove that: cosh (x + y) = coshx coshy + sinhx sinhy %3D

A: We know that cosh(θ) = eθ+e-θ2sinh(θ) = eθ-e-θ2

Q: Let -(x) be the Taylor polynomial of degree for the function x) = cos(x) at = 0. Suppose you…

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Q: 3. Find the root/s. (Use Bisection Method) F(x) = (x/2)² – sin(x)

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Q: Estimate the root of the expression, f(x) = x* – 4x, using: a. Bisection Methodin the interval [0,2]…

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

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.