A cubic spline S is defined by: So(x) = 3(x- 1) + 2(x – 1)² – (x – 1) S(x) = s,(x) = 4 + 4(x – 2) – (x – 2)² +(x- 2)* if 1 SxS2 if 2 SxS3 S is a natural cubic Spline O False True

Q: (1+x(2)- 2x(2)(1 + x)(2x) (1 +x)*

A: Apply BODMAS rule, to simplify the given expression. First, remove the parenthesis and then…

Q: Consider the points (x₁, y₁) (-1,6), (x2, 12) (0, -2), (x3, 13) (1,4), (X4, Y4) = (2,4). + = x + =…

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Q: 2 17. The polynomial P(x) = x* - &x – of x = 1, 3, and -2+i. What is its fourth zero? 8x +15 has…

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Q: a) Show that f(x) = |x|Vx8 + 1 is an even function. b) Find the end behavior of f(x) = -(x – 2)*(x +…

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Q: Find k so that kt² – 5t – 12 is in span{4t² + 3, −5t² − 5t}. -

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Q: Q.9 Using remainder theorem, check whether p(x) is a multiple of g (x) or not. (i) p(x)=x' -5x² +…

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Q: (4) Given f(x) = x³ – 6x² – x +6. a) (2 pts) Use the leading term to determine the end behavior of…

A: The end behavior of a polynomial f(x) is the behavior of the graph of f(x) as x approaches to +∞ or…

Q: te a polynomial function with zeros -3, -12 and v2 A) p(x) = x² - 2r – 6 Final Exam Math 001 Term…

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Q: 3. (12 points) Given f(x) = −0.25x3(x − 2)² (x + 1)4 - Find all of the zeros and state their…

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Q: The zeros of the polynomial P(x) = x³ – 2x2 + 4x - 8 are %3D La)-1,2i, and - 2i (b) 1,2i, and – 2i…

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Q: 6. Suppose the polynomial function has the given root. Find the other roots (a) f(x) = 2r3 – 4x2 –…

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Q: Find the 1-/2a2-1 limr 1 x-1 O 1 O -2 None of these

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Q: Given f(x) = - 3x*(x + 2)*(5x + 3) (x – 2)5 List the zeroes (ex. 4, 6, -2): -2,-.2 Degree: 15 End…

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Q: Which polynomial function has the following end behavior? Assume a and k are positive constants. If…

A: Given: If x→-∞ then p(x)→+∞,   If x→+∞ then p(x)→-∞

Q: 29. The area of the shaded region shown below can be represented as (2x + 6) (2x + 6) - (r(x + 3)²).…

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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 g(x) = 4x3 + 4x - 10x2x3 be a quadratic form in three variables. Find a quadratic form of the…

A: Given: g(x)= 4x22+4x32 -10x2 x3 The matrix of the…

Q: 2. Identify the approximate input values of any relative maximums and minimums of this 5th degree…

A: I am going to solve the given problem by using some simple algebra to get the required result.

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

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Q: t is known that the polynomial p(x) = 2- (r+ 1) + x(x+ 1) – 2x(r + 1)(r – 1) interpolates the first…

A: Given:- p(x)=2-(x+1)+x(x+1)-2x(x+1)(x-)  interpolates the first four points of the table. x -1 0…

Q: How many zeros (solutions) does the following quadratic relation have? f(x) = x² + 2x + 2

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Q: Given f(x) = 2(x - 1)(x + 3)³(5x + 1)^(x − 3)¹ List the zeroes (ex. 4, 6, -2): Degree: End behavior:…

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Q: The envelope below has a mailing label. L(x) = 6x + 5

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Q: 3(2x +1) x+3x +x-6' a) Given g(x) = %3D x> 3. i) x+1 Show that g(x) = x>3 x-2 ii) Find the range of…

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Q: Determine Number of Zeroes Num of the Polynomial function: F(x)=x²₁²-9x Zero (5)

A: We have to find zeros

Polynomials

Try substituting 1. You will get 6 and not 0. Try other real values also. What About -2? Let us check.