Exercise 5: Given the table of the function f(x)=2* 1 2. 3 8 f(x) 1 2 4 a) Write down the Newton polynomials P1(x), P2(x), P3(x). b) Estimate f(2.5) by using P3(x). c) Obtain a bound for the errors E1(x), E2(x), E3(x).

Q: Find maximum and minimum values of the function 2х + 1 2 3

A: fx=13x3-12x2-2x+13 Differentiating wrt x, we get f'x=x2-x-2                                   (1)…

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Q: 2十 1. t. a) Express f(t) in terms of unit step functions

A: To express f(t) in terms of unit step functions.

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A: T(x)=x+9x73-2x25Formulaamn=amn1at=a-tddxx=n xn-1

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Q: Q7. Check if the following functions are Orthogonal or not? fi(x) = x°, f2(x) = x² + 1 [-1, 1] on…

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A: given: Hx=1-x2 we have to find the functions f and g so that f ∘ g = H.

Q: determine the value of the parameter a that will make the function f(x) = [ax+1, x- -1

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Q: Find the local extrema points of the function f(x)=(x−a)ex, where a is an arbitrary real number.

A: Consider the function

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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: Let f(x)=x² + 5x + 1 and (t) = n(t) + et. Use your calculator to evaluate the following valuesounded…

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Q: Let f(x) = 5- x and g(x) 2, find: a. (fog)(0) b. (go f)(0) = c. (fo g)(x) Preview d. (go f)(x) =…

A: Value of the above ques is

Q: Write the domain in interval notation. 3) y (t)=√√√8-t 4) f(x) = x - 4 x-5

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Q: Find f such that f′(x)=8x​, ​ f(4​)=47.

A: Given, f′(x)=8x​,​ f(4​)=47.

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Q: Compute f(5) (e) forthe function f(x) = x³.In(x+)

A: f(x)=x3.ln(x4)f(x)=4x3ln(x)Differentiatef'(x)=4x2+3x2ln(x)f'(x)=4x2+12x2ln(x)Differentiatef''(x)=8x+…