Consider finding the root of f(x) = e-x(3.2 sin x - 0.5 cos x). a. Use Bisection Method with a stopping criterion of for 0.0001. b. Use False Position Method (Use tolerance level of f(c) < ε = 0.00001)

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A: Given f(x) = 3x3 + cos(3πx) + 2x,  x≥1   ⇒ f'(x) = 9x2 - 3πsin(3πx) + 2

Q: 18. Find relative extrema of f(x) = sin where function is increasing. cos x, over the interval , .…

A: Given fx=sinx2cosx We have to find the relative extrema of fx=sinx2cosx over the interval -π2, π2.…

Q: 1. f(x) = sin 2x + cos 3x + x² = 0 with xo = -0.5 , Ax 0.1, TOL = 0.001, in [-0.5,1] %3D

A: Given equation is fx=0 where f(x) is defined by fx=sin2x+cos3x+x2  Given initial solution is x0=-0.5…

Q: 3. Find f'(x) if f(x) = 2x + sin³ x

A: Here we use the quotient rule of derivatives. It says ; d/dx (u/v)=( v*u'-u*v' )/(v^2) Where u and v…

Q: Verify the following properties for ƒ(x) = sin x and p3(x) = x - x3/6:                    ƒ(0) =…

A: We first find the derivatives

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A: Equation is f(x)=ecos(x).The value of the table for x and y x 0 0.25 0.5 0.75 1 1.25 1.5 y 2.72…

Q: 1. Find all critical numbers of the function f(x) = 1/3 sin (6x) -x, on the interval 0<x< Show all…

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Q: 4. Write a script which uses finite difference approximations to compute the first derivative dy/dx…

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Q: Find f(x), where f'(x) = sin(x) + cos(x) + 1 and f(#)=2. %3D %3D

A: Using anti derivative formula.

Q: *Use the functions below for the next three questions f(x) = 4 sin (2x –) + 4 and g(x) = -6 cos (2x…

A: Solution is given below:

Q: Sin x3D%=

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Q: Bisection method was used to determine a root for a function f(x), using initial interval (x1, xµ)…

A: Consider the given information. Let the Initial interval be (xl, xu) Then h=xl-xu Which is the…

Q: Suppose that f(x + h) – f(x) =-7hx + 8h – 2h?. Find f'(x).

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Q: 1. Find the centered difference approximations of 0(h^4 ) for the first derivative of y=sin(x) +…

A: As per the policy, we are allowed to answer only one question at a time. So, I am answering the…

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A: Given:  a) fx=sin2x+3x2+1 b) fx=x2ln4x-1 c) fx=x2+3x+2 To determine: The value of f'x.

Q: 2. Find f35 (x) and f102 (x) for f(x) = sinx. 3. Find f'(0). f(x) = sinx + 3 tan x + 1

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Q: C) It is given that f(r) = tan¯*(1 +x). (i) Find f(0) and f '(0), and show that f "(0) =

A: Given Fx=tan-11+xwe find F0,F'0 and prove F''0=-12

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A: Consider the given function  f(x)=lnx-cosx with initial estimate  po=1  ,        p1=1.2

Q: Which of the following is represents an estimate of L sin(x) dx using rectangles with heights…

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Q: 4. Let f(x)= 5Vx and g(x)= 4 + sin x. (a) Find (f ° (x) and (f ° g'(x). (b) Find (g ºf)(x) and…

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Q: Find A and B if the function 3 sin?(4x) sin(6x2) ' if x 0. s continuous.

A:

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Q: Let f(x) = 3 cos 2x + sin² x. a) b) Show that f'(x) = -5 sin 2x. Зл In the interval <x< one normal…

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Q: 2sim x-1 -y = COST+2

A:

Q: f(t) = (cost, Sint, t) f'(t) = (-sint, west, 1) 1 f'(x)) = √√(-sint) ² + ((ost ) ² + 12 F(t)= -…

A: Given that Differentiate with respect to t           Therefore