This piecewise polynomial is NOT a cubic spline: if 0sx<1 if 1sx<2 %3D S(x) = So(x) = 6 S, (x) = 6+ (x- 1)2 Why not? So"(1) # S,"'(1) S" (1) # S{"(1) This option This option So(1) # S,(1) So'(1) # S,'(1) This option This option

Q: 1. Lim 2 x+3x+1 7x²-2x+4

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Q: (x²+4x-5)¹/2 lim x→1+ (x²-4x+3)

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Q: lim, 1 2²-7x+6 z-1

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Q: The limit when x approaches to 5 of a polynomial f(x) is f(-5)

A: Given The limit when x approaches to 5 of a polynomial f(x) is f(-5)

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Q: The DaveCo Giant Robot division finds that its profit P, (In millions of dollars) is a function of…

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Q: (x² – x – 2)(2x +3). Vx² +5-V3x +3 6. lim =... .2 x2

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Q: lim

A: We have to evaluate the following limit: Limit as x tends to -infinity (2x + 1)/[sqrt {7x^2 - x +…

Q: Enter the zeros of each polynomial together with the zeros of the first derivative. a) y=x² - 4 b)…

A: Given: a. y=x2-4b. y=x2+8x+15c. y=x3-3x2+4=(x+1)(x-2)2 d. y=x3-33x2+216x We are required to find:…

Q: x*+6x3-1 4. Let p(x) = x5 + 3x² – 1 and r(x) = - x²+x-2 a. How many zeros could p(x) have and why?…

A: We have to solve first 3 parts according to the guidelines.

Q: x2-4 lim x--2 x2+4x+4

A: In this question, we have to find the limit of a function which is of the form 0/0.

Q: XVI+T(1-V2x+3) 7-6x+4x Compute lim

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Q: Which of the following statements is true? 7x2 7 A lim 3 (ку) - (0,0) Зx2 — 5ху+ 2у Зx+у-4 lim 8…

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Q: If p(x) is a polynomial in Zp[x] with no multiplezeros, show that p(x) divides xp^n-x for some n.

A: Px is a polynomial  Px=x-ax-bx-c...x-ux-vx-w where   a,b,c...∈Zp but u,v,w∉Zp Let Rx=x-ux-vx-w has…

Q: √x-10 lim x-100 x-100 lim x→4 2 x² - 2x-8 x² -16

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Q: 2x – -12x + 40 3x2 + x – 14 14) lím エ→2

A: We will find the value of the limit as following.

Q: (2x- 1)1/2 – 3 Lim X-5

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Q: 6xh + 3h2- 5h lim h-0

A: On directly substituting the limit, the indeterminate form 00 will be obtained. So, in such a way…

Q: Find the following using the rule indicated (only): i) If f(x) = (6x? – 8) (3x + 2), find f'(3)…

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Q: (b) lim In(5x2 +3) – In(2r² + 1). -

A: Given :

Q: x6 – 3,000x5 lim x→-0 4x° + 10,000 9

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Q: Example 48 lim,→∞(Vx² +x – Væ² + 5) =?

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Q: 1– x2 lim r--00 3 + 2x – x3

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Q: Show that the polynomial p(x) = -x^3+x^2+1 has a root in [1,2]

A: We can check for the values of p(x) :

Q: ..... ..... If a and b are constants and lim asin(4x)-btan(8x) 3, x → 0 4xcos x+8sin(12x) then a-2b=

A: Solution is given below:

Q: (e) lim V9r2 +x-3r %3D

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Q: Write a polynomial function in standard form with zeros at 2, 4, and 5. 0 (2) = 2 382 + 11a 40 %3D…

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Q: Which of the following are vertical asymptotes of f(x) = x2 - 2X 7 x² – 4 x=0 x=-1 x=-2 X=1 x=2

A: Recall:  To find vertical asymptote, set the denominator equal to zero and solve for x. Given,…

Polynomials

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