Consider the function f(x)=5⋅x3+3f(x)=5⋅x3+3 over the interval [2,4][2,4]. Partition the interval up into eight equal subintervals. What are these subintervals: Input the intervals with the endpoints in ascending order. rational numbers only    Consider the fourth of these subintervals. Letting c=11/4 estimate, by use of the appropriate rectangle, the area under the curve of f(x) in this subinterval. area estimate =

Q: B) Estimate the next root of the function f(x)=x^3-x-1 using Muller method, let x0=1, x1=2, x2=1.5

A: Muller method: The Muller approach is applicable to any root-finding programme, but it is especially…

Q: Given f (x) =r - 4r defined over [1, 3]. Using Secant :method, the first approximated root for f(x)…

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Q: Let L(x) = ln(x² + 4x + 14) in the interval [-10,10]. What are the absolute extrema of L(x) in this…

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Q: By using the demition, Calculate the dervedves of the functions |- }cx) = 4 - x* ; F'(-3) ,f'c1) 2.…

A: Differentiation is the rate of change in the value of dependent variable with respect to the change…

Q: 16. If f(x) = 2x² + 3x + 5, f(c) = 20, and the interval is [0,5], use the Intermediate Value Theorem…

A: If fx=2x2+3x+5,  f(c)=20,  [ 0,5]  f0=202+30+5 = 5  f5=252+35+5 = 70  Using Intermediate value…

Q: a. Find the value of (k) that make fhe fimction contimuous at x = 0 3k -3 =0

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Q: 1) For the function f(x)=10-0.1x² +1.6x² – 4.8x on 0<x<10 and n=5: Begin by calculating Ar and…

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Q: 8. For the given function f(x) = v1+x, let ro = 0, x1 = 0.6, and r2 = 0.9. Construct an…

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Q: 02: Let f(x)= x' – 7x+ 2, 0sxs1. 1. Show that f(x) has exactly one real root in the indicated…

A: Answer

Q: Determine the degree of the Maclaurin polynomial required for the error in the approximation of the…

A: Maclaurin's Series of f(x) f(x)=f(0)+xf'(0)+x22!f''(0)+ ⋯ +xnn!fn(0)+Rn(x)…

Q: Given the function f(x) = 2x3 – 11.7x? + 17.7x – 5, find one root using Secant Method with an…

A: Consider the given equation, fx=2x3-11.7x2+17.7x-5 Now, define the secant method.…

Q: Use the second serivative test to find the local exterma of the function f(x) =x3+12x2-5 on R

A: If second derivative negative then maxima and if positive then minima

Q: Find the critical numbers of the function f(z) = 2x'-24r. Answer (separate by commas): I = Il

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Q: Find the nth Maclaurin polynomial for the function. f(x) = sin(x), n = 5 1. 2 1- x+ x - 1.4 24 1 5…

A: We have to solve

Q: 1. Suppose that f f(x) dx = In x + Vx+1+C. Can f be a rational function? Explain.

A: To explain f is a rational function or not.

Q: Given f(x) = In(x² + 3x + 9), over the interval [ – 5, - 1], answer the following: %3D a) The point…

A: Given,           fx=lnx2+3x+9

Q: Determine the degree of the Maclaurin polynomial required for the error in the approximation of the…

A: Given f(x)=sinx We have to determine the degree of the Maclaurin polynomial required for the error…

Q: Consider the function f(x) = ex – 1, the third approximation of the zero p, of f using Nweton's…

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Q: Define f:R → R by f (x) = 5x if x is rational and f (x) = x² + 6 if x is irrational. Prove that f is…

A: Given, f:R→R by f(x)=5x if f(x) is rational and f(x)=x2+6 if x is irrational.To prove that f is…

Q: Q4) Find the root of f(x)= (x^2)-5, in interval [0,4] by using bisection method.

A:

Q: 2. For the given functions f (x), let.x, = 1,x, = 1.25, and.x, = 1.6. Construct interpolation…

A: Step:- 1 Lagrange Interpolating polynomial:- P(x)=f0 L0(x) +f1 L1(x)+ f2 L3(x)+....fn Ln(x),Here,…

Q: (a) Let x2 if x is rational f (x) = 0 otherwise. Prove that f is differentiable at 0.

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Q: Find the Chebyshev rational function approximation of the function f (x) = e=* in N =6 (m=3 and n=3)…

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Q: The absolute maximum of f(x) =x² – 4x on [0,3] is y= OA. OB. 4- o 3- OC. OD. 0.

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Q: Consider f(x) = x^7 + 2x^4-1, 0 = 1. Differentiate f at x = 0:5 using 5 point formula. Also…

A: TThe 5 points central difference formula is f'(x)=f(x-2h)-8f(x-h)+8f(x+h)-f(x+2h)12h. Here, h is the…

Q: For the given function 1 (x)=sin x, let x, = 0, x, = 0.6 and x, = 0.9. Construct the Lagrange…

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Q: 3. Consider the function f (x) = 2 x + 1 on the interval [2, 6]. (a) Compute the left-endpoint…

A: Solve the following

Q: Given f(x) = r³ – 2x2 – x + 2 on [1,2]. Verify the three conditions of the hypothesis of Rolle's…

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Q: Use the Bisection Method to find a zero of f(x) = -x³ + 4x – 7 on the interval [-3, –2] (three…

A: Given function is f(x)=-x3+4x-7 First iteration: f(-3)=8&gt;0; f(-2)=-7&lt;0 c0=-3+(-2)2=-2.5 Second…

Q: is continuous and integral 3 to 1 f(x)dx =8, show that the graph of f intersects the line y=4 at…

A: Given that f is continuous and f13f(x)dx=8 To prove line y=4 intersects the graph of f altleast can…

Q: t 0, if x is irrational 1, if x is rational ve a rigorous proof that f is not integrable on the…

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Q: For f(x) = = 0 with xo = -2, find the estimated root using NRM if the stopping criterion-is…

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Q: III. Let f(x) = e2 sinz 2. Find the absolute extremum values of f on the interval [

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Q: The function f(x)=/25-x' is contionous on

A: It is continuous function.

Q: Consider the function f(x) = 8 – 8x2/3 on the interval [-1,1]. Which of the three hypotheses of…

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Q: Let f be the function defined on [0, 1] by when x is irrational, f (x) = 1 when x is rational.…

A: Please see the below picture for detailed solution.

Q: Given f (x) = r – 4x defined over [1, 3]. Using Secant :method, the first approximated root for f(x)…

A: Consider the given function, fx=x3-4x The given condition is [1,3]. The secant method is defined as,…

Q: Let f(x) = e2X be a function approximated by a polynomial Pn (x). If P, (2.5) =0.00687, what is…

A: We know that Absolute error is the absolute value of difference of measured value and actual value.…

Q: (b) Given f (x) = x – e-², use the Bisection Method to approximate a root of f on [0, 1], accurate…

A: Since you have asked multiple question, we will solve any one question for you. If you want any…

Q: (b) Given f (x) = 1 - e², use the Bisection Method to approximate a root of f on [0, 1], accurate to…

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Q: If f (x)  =In  (2x + x Sin x), use the graphs of  f ,f' , and f"to estimate the intervals of…

A: Given: f(x) = ln(2x+xsin…

Q: Describe the concavity of the graph of f(x) = x2-sin(2x) on the interval [0, π] on(4);concave down…

A: Obtain the first derivative of the function f(x)=x^2-sin(2x).

Q: 19. Any rational function of the form f(x) where b 0, always has a y-interce %3D

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Q: Consider the function f(x) = x² – 4x + 4 on the interval [0, 4]. Verify that this function satisfies…

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Q: (a) Let | x² if x is rational f(x) = otherwise. Prove that f is differentiable at 0. (b) More…

A: at first we check the functions are continuous or not. If the function is not continuous at the…

Q: A. Compute the bound B of the error when approximating f(x)=sin(x) with a polynomial of degree 1 in…

A: The given function is fx=sin x. Find the error bound for f approximating with a polynomial of degree…

Q: Consider the regular subdivision of the interval [a, b] as a - x0 < x1 < x2 < x3 < 14 = b, with the…

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Q: Consider the region bounded above by g(x)=−9x−9 and below by f(x)=x2 −9x−18. Find the area, in…

A: Calculation:The given curves are f(x) = – 9 x – 9 and g(x) = x2 – 9x – 18.The area enclosed by two…

Q: The function f(x) = x³ – 3x² + 5 is concave upward on the interval O (-∞, 1) (1, co) (-∞0, ∞0) O…

A:

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.