In a cubic spline approximation assume that we know that S;(x) = 4 – 5x+ 2x² + 3x³ Si+1(x) = a + bx + cx² + 3x³ if 1< x < x;+2 if x;

Q: B) Test the functions continuity at the given poihts: (x²-x-6 1) f(x) 3D x * 3 ,at x 3, x 5 X-3 x =…

A: f(x)=x2-x-6x-3x≠35x=3

Q: ) Prove that sech¯¹(x) = In ( ¹+ √¹-x²) X

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Q: JUX² +2x-8 dx Evaluate lx + 1Wx + 1)* + 9 = l(x + 1) + Vtx + 1}² – 9|]+c 9ln (+ 1)/(x + 1)² – 9 –…

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Q: Prove that VÃZ,n,m=N(x²)m = xmn¸

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Q: Determine a value for m so that h (x) = -1/3 x^3 + nx^2 + 8x – 15 has an inflection point at  x = –…

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Q: The solutions of cosh(2x) = 8sinhx - 5 are a) x = ln (4+ √17) and x = ln (1 + in (1 + √2) b) x = ln…

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Q: Solve if w be cube root of unity then (1+w)(1+w^2)(1+w^4)(1+w^8).....2nfactor=1

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Q: Find all solutions of csc(x-3)=(2(sqrt(3)))/3 on the interval [4pi, 6pi] x= ?

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Q: lim x→-3 √x²-5-2 x² + 2x -3 - 2. lim t→1- 2 2t² - 3t+1 1 t² - 3t+2,

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Q: 8. lim x 0 √x²+4-2 x2

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Q: f(x) = -(x ² + x-30 (x, f(x) Axis of symmetry: ● X-int (smaller) x-int (Larger) Form: Standard •…

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Q: a) 6e2x – 17(e*) + 12 = 0 b) 82x+1 = 45-x %3D

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Q: 1. Expand (r+ 1)(x – 2)(x + 3)

A: We will explain this using commutative law and associative law of multiplication.

Q: A solar oven is to be made from an open box with reflective sides. Each box is made from a 30-in by…

A: Note: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question…

Q: consider the degree 4 LFSR given by polynomial p(x)=x^4+x^2+1. What kind of polynomial is this…

A: The given polynomial p(x)=x^4+x^2+1 With 4 LFSR.

Q: alvale the 3x2 -x +1 1) (x2+4)

A: Ans is given below

Q: A Moving to another question will save this response. Question 10 "The product of a negative real…

A: Let us assume a negative real number x. So, x&lt;0 And a positive real number y. So, y&gt;0

Q: Show that: n n > (xi – x)2 > x? – n(x)2 | i=1 i=1

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Q: 2 ln (1+√√y) = 2 ln (1+√√x) + In C n{(1 + √y)²} = ln {C(1 + √@)²}

A: Given that 2 log 1+y=2log1+x+log C Here we need to explain the next steps.

Q: Consider the following. 3x4 - 8x + 5 = 0, [2, 3) (a) Explain how we know that the given equation…

A: Given that  3x4−8x3+5=0, 2,3

Q: Let f(x)=x*-2x. Use cubic Lagrange Interpolation based on the nodes Xo =-1,X1=0,x2= 3,X3=4 to…

A: Given, fx=x4-2x3 x0=-1, x1=0, x2=3, x3=4 To approximate the value of f3.5.

Q: Given that f(x) = 7x + 5 and g(x) = 8 – x², calculate (a) (f o g)(0) = f(g(0))= (b) (g o f)(0) =…

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Q: 2. Prove or give a counterexample to • If X ≤Y then Var (X) 0 . Var (X) ≤ Var(X)

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Q: Let S,(x) = 2x³ – 3x² + 3x – 4, 0<x < 1, S,(x) = x³ + b,x² + c,x + d,1 sxs 2. Find b,, C1, d, that…

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Q: Integrate the function. √√36-x² dx O 18 sin O sin ¹ (-2) + x√/ 36 - x² + C +C 2 O 36x √√36-x²…

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Q: ¸¸ S'√ 16–16 x² d x = · (a) 16 π (b) π square unit. ©2π (d) 4π

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Q: -Vx2+5 -x f(x): f'(0)? -x+2

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Q: The quadrature rule [“ f(x)dx = w₁ f(x1) + w2f(x2) + E (2) -h can be made exact for all cubic…

A: Given Information:The quadrature rule is given as .Objective:Write the four equations satisfied by…

Q: Let f(x) = x5 + 3x4 + 2x2 and f(z) = 1024 + 1232i, the value of z is O2+4i 2-41 3+21 1+2i

A: Given the function  and .The aim is to find the value of z.Used Formula:Note:

Q: Find the multiplicity of each given zero of f(x) Modified Newton-Raphson's method to approximate the…

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Q: 10) Use Lagrange coefficient polynomial L3,2(x) to find L3,2(5) using the nodes Xo = 3,x1 = 4, x2 =…

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