When using divided differences to compute Hermite splines, we defined a divided difference with two identical arguments f[x,, z] as the limit: f(x,x] lim fx₁,x] and used this definition to show that f[x₁₁x₁] = f'(x₁) = y₁₁ (a) Let a divided difference f[x,,,,,] be defined as the limit: f[x₁, x, xi]:=lim f[xi — €, x₁, xi + e] Show that f[a,,a,,a]=f"(x) = . You may use (without proof) the following limit: f(x-e)-2f(x) + f(x+e) f"(x) (b) Explain how Newton interpolation and divided differences can be used to compute a cubic polynomial s(ar) over [zo, z1] such that lim €0 s(xo) s'(zo) s" (xo) s(x₁) Yo % Yo 9/1

Q: Find the limits

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Q: Suppose thatƒ and g are functions such that lim f(x) = 9 x →4 lim g(x) = 4 Evaluate the following…

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Q: Evaluate the limit: lim x+7 sin x Оо ○ 1 ○ 2 4 x→0 sin 4x

A: lim x approaches to 0 (x+7sinx)/sin 4x = 2 (4th option is correct)lim x approaches to infinity ln2x…

Q: State the definition of the "limit of a function": The definition begins: VEN: f:(x1,a)U(a, x:) – R…

A: The definition for limit of a function: The number L is called the limit of a function f(x) as x→a…

Q: Consider the function f(x) = {,* - a, -1<x< 2 lb – 2x, 2<x<4 If b =1 and the limit of f (æ) as æ → 2…

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Q: Use two different paths to demonstrate that the limit: lim(7,9)→(0,0) x*y?+(x=y)?

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Q: 23) lim f(x) x→1- f(x) 5- 4+ 3+ 2+ -5 -4 -3 -2 -1 -1. 5 х 2 4 -2+ -3+ -4+

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Q: Find the limits of the following functions: a) lim 2x + |x – 3| x→3 Vx2+9–5 b) lim x→-4 x+4

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Q: 10. Use the definition of limit to show that a. lim (x² + 4x) = 12, Z-2

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