In the Secant Method of numerically finding a root of a function, the algorithm for iteration is: Xn – Xn-1 Xn+1 = Xn - f(Xn) F(xn) – f(xn-1) ow that this can also be written as: Xn-1 f(xn) – Xn • f (xn-1) f(xn) – f(xn-1) Xn+1 =

Q: Find the min and max of (f)

A: This question can be solved using the concept of maxima and minima.

Q: If f(n) and g(n) are multiplicative functions, and g(n) does not equal 0 for all positive integers…

A: Definition 1 : A function f: ℕ→ℂ is said to be arithmetic function .   Definition 2 : An arithmetic…

Q: consider the polynomial equation x3-7x2+14x-4=0 over the interval [0,2].

A: Iteration formula: The iteration formula of secant method is pn+1=pn-1-f(pn-1)pn-pn-1f(pn) -…

Q: Given s(x)=(x-2)2, find s(4), s(-3), s(2), s(1) and s(0) and find the domain of s.

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Q: Let 2 f(x) = a² + 9 and g(x) = /3x – 5 If h(x) = (f o g)(x) and k(x) = (go f)(x) then h(3) and k(3)…

A: Composite functions

Q: If f(1) 10 and f(n) = –3f (n – 1) + n then find the value of f(4).

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Q: The interpolating polynomial p(x) of degree 2 of f(x) = 6xª – 2x³ + x² + 9 is p(x) = x² + 9. %3D…

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Q: Consider f (x) = ka + 3 and g(x) = 22 - 3x +2. If f (g(-1)) = 9, then k = If f (z) = and g (z)…

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Q: Use Fermat's Theorem to find a number x between 0 and 28 with x 85 congruent to 6 modulo 29. (You…

A: as given  x85≅6mod 29   ...i as we known 29 is a prime number  by fermat's little theorem if p is a…

Q: If f(x) 52-8 ²-8 f (4x) + 1 = for x + √8, what is ƒ (4x) + 1?

A:

Q: If f(1) = 4 and f(n) = f(n – 1) + 3 then find the value of f (4).

A: Given f(1)=4, f(n)=f(n-1)+3

Q: (d) Compute P(x 2 2).

A: Given that  X~Poisson(μ=6) Probability mass function of X is  f(x)=μxe-μ/x!  , x=0,1,2,3,____

Q: Given the function k(x) - Calculate the following values: k( – 9) = k(2) = k(4) = k( − 8) = k( − 1)…

A: Here we have to find the values of a function.

Q: Consider the function x + 5x-6 S(x) = x2 +4x If it exists, give the equation of the horizontal…

A: A function is usually represented as f(x) where x is the input to the function and f(x) represents…

Q: Using P3(x) =[5x³ – 3x] and P4(x) =[35x* – 30x? +3], generate the next Legendre polynomial using…

A: It is known that the Legendre polynomial satisfies the following recurrence relation.…

Q: Find f (x) for f(x)=-- O f-¹(x) = -5x2 O = f-¹(x) 2 5x+3 O f-¹(x)= 3x 2 O f-¹(x) = 5x-3 -2x 5x-3…

A:

Q: W= Sp { (2,0,-1,2), (d,d, 2,3) } cR find a basis for the oahogonal complement of the Ssubspace w

A: Given below the detailed solution

Q: Find (f – 9)(x) if f(x) = -3a? + 2x – 3 and g(æ) = 2x2 – 3x + 4. O (f - 9)(x) = 5x² – 5x + 7 • (f –…

A:

Q: (a) Write down the piecewise form for the function |2x – 3|. (b) Hence or otherwise find all…

A: we have to write the given function in piecewise

Q: f(x) = { kx+3, IF X<2 LyK-3x, IF X72

A:

Q: Use the given definition to find f(A): If f(x) = a + a₁x + a₂x². + ... + anx is a polynomial…

A:

Q: The following polynomial relates the specific heat to constant pressure of dry air Cp (in KJ/KgK),…

A: Given: Cp=1.2 KJ/KgK. Substitute the value of Cp in…

Q: Find f(k-1) when f(x) = 5x² + 4x + Of(k-1) = 5k² - 6k + 10 f(k-1) = 5k² - 6k + 2 f(k-1) = -6k² + 5k…

A: Introduction: A polynomial function is a function that involves only non-negative integer powers or…

Q: Determine the partial fraction expansion for the rational function below. - 19s + 75 (s+5) (s² +9) -…

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Q: f(0.5) = 0 and f( -1) = 6 indicates that: * O There is no remainder when f(x) is divided by 2x - 1 O…

A: Answer is first option.

Q: (a) Show that for n> 1 we have F2 = FnFn+1 − FnFn-1. (b) Use part (a) to show that F² + F² + . + F²…

A: Fn denote the Fibonacci sequence, satisfies Fn+1=Fn+Fn-1.              n≥2 And         F1=0,…

Q: If g(x) = [ √(x - 3) if x≥3 or 3 - x if x &lt; 3] , find g(-1) and g(7).

A: Guven function with intervals --g(x) = x-3    when  x≥3                   ...................(1)g(x)…

Q: Which polynomial function in standard form has a root of multiplicity 1 at x= 3, and a root of…

A: A polynomial function has a root of multiplicity 1 at x=3, and a root of multiplicity 2 at x=4

Q: Let f(x) = 2x + 3 and g(x) = 5æ² + 4x Compute and simplify the following. (f + g)(x) =

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Q: Consider the following problem: max(x + 1)(y + 1) {x,y} x + y< 10

A:

Q: If E[X 4 and Var(X) 1, then E(1 + 5X)²] - and Var(2 + 4X)

A: GivenE(X)=4Var(X)=1

Q: Find f(x + Ax) by substituting x + Ax in place of x in f(x) = 9x² - 5x. f(x + Ax) = 9( x+ Ax D² - 5(…

A: To find the f(x+∆x)