3x + 7x2-5x-4 Let f(x) = %3D 6x +4 1. Use Ad-hoc calculations to prove that f(x) is O(x2) 2. Use limits to prove that f(x) is O(x2)

Q: ivative of p = 2xz nes maximum in t 3k

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Q: Vx2+3 lim X-

A: limx→∞x2+3x=limx→∞x2(1+3x2)x=limx→∞x(1+3x2)x                         =limx→∞ (1+3x2)     =1

Q: - e4 7. lim. x-2x² - 2x ex2

A: We have to find out limit

Q: Find the limit.

A: Our Aim is to find the limit of the expression given below:-limx→3 x2-3x+4 -(i)

Q: 3x2 + 7x – 2 7) lim x-1 3x²- 4x – 2 7) A) 0 B) Does not exist 8 D) -

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Q: 4x3 + 6x² – 2 18. lim x→-o 2x3 – 4x +5 x2 22. lim xH0 Vx4 x+ 3x2 26. lim хн00 4x — 1

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Q: 4 2 . 02- 9f 2xS 9x) s X-X+2 lim

A: Given: 2x≤gx≤x4-x2+2

Q: Find the linearization at x = a. f(x) = 7x³, a = 1 (Use symbolic notation and fractions where…

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Q: 4. Find the absolute maxima and minima for f(x) = 4x - 9x2- 12x-1 on the closed interval [0, 4].

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Q: 2n lim 4k2 + 3n2 k=1 n00 tegral

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Q: Consider the following equation. 3x4 − 8x3 + 8 = 0, [2, 3] (a) Explain how we know that the given…

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Q: dass limits a4-07 f ļ of 9kー101 102-105 I06-109 110-13 14-117 13

A: Solution Mean=103.57

Q: EXERCISE 4. Evaluate the following using Rationalization Method. Show your solution. Vx² + 7 – 3 lim…

A: Given  The limits are 1.  limx→3x2+7-3x+32.  limx→0x+1-1x

Q: f(x) = 4x - 1.8x2+1.2x3-0.3x4 Find the maximum using Parabolic Interpolation (X0= 1.75, X1=2,…

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Q: 8+x-4x? Lim\ belowr → 0∞ V6+x²+7x* O a. -4/7 O b. 4/7 O c. 4//7 O d. -4/7

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Q: Jse f(x) = x²-x, g(x) = 9 – 2x, and h(x) = x² + 2x-63 Evaluate (go h)(-1)

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Q: 3x+x Q2) Evaluate limy+o 2-8

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Q: x2-9 is x→-3 V 2x2+7x+3 V30 lim V20 D. Е. О A. no limit B. С.

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Q: (のx -8) ( 5x° ran-3) Cメ2ムx) lim メJ 8

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Q: Find the linearization at x = a. f(x) = 9x*, a = 1 %3D (Use symbolic notation and fractions where…

A: We have to find the linearization of the given function.

Q: 2 Find the limit infimum and supremum of 2 XA = √√√ 1+n² √1tn 2A-5 write the complete solution.

A: Limit infimum and limit suprimum

Q: @ f(x)= x²-3x-4 2 @ f(x) = x² - 4x +3 Show that whether f(x) reduceable Poly or not

A: The given problem is solved below in detail.

Q: Suppose h (x) = ax³ + 11x². Determine a if h has an inflection point at x = 4. Show all your work.…

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Q: hg limits exactly. x3+3x2-11x-68 lim x2-7x+12 X4

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Q: ind the Wronskian of: 18x - 6 18x + 6 6x - 18 6x + 18 f₁ = x² - 6x f₂ = x² + 6x f3=x²-3

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Q: 8. lim (2x – V9x² + x + 5 n-+00

A: limx→∞2x-9x2+x+5

Q: бх — 2, х < 2 3. limf(x) for f (x) = x-2 %3D 13x2 -1, х 22 |

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Q: a) Evaluate V9x(x² – 3x +2) lim (3х — 3)

A: To find the limit:

Q: 7. Find k so f (x) = x*. kx3 + kx2 + 1 has a factor of x + 2. %3D

A: f(-2) =0

Q: = -5. Let p2(x) be the interpolating polynomial of f(x) at xo = Then, the error term in…

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Q: 5. Find limf(x) x4-3 a) f(x) = 5x4 %3D 6x4 - 3 b) f(x) = 3x3 2x3 - 9 c) f(x) = %3D 3x5

A: We have to find limx→∞fx for a fx=x4-35x4b fx=6x4-33x3c fx=2x3-93x5 Since all above limit has ∞∞…

Q: Find the linearization at x = a. f(x) = 3x², a = 1 (Use symbolic notation and fractions where…

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Q: Consider f(x) =x³ - 6x2+9x + 3 defined on the closed interval . At which value of x does the…

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Q: Verify the assertion made in Example 2.

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Q: 6) lim х-1 3x+2 6) А) 0 C) does not exist D) 1

A: Please see the answer below.

Q: 2. lim g(x) for g(x) = { (-6x + 2x if x <-2 3x2 – 3 X--2 if x 2 -2

A: The given function is g(x)=-6x+2xif x&lt;-23x2-3if x≥-2 We have to find the limx→-2g(x)

Q: 2. Find a polynomial that interpolates (-1,4) and (3,6), then find the value of f(x) at x=0 and x=…

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Q: 3x 2+13x+4 p. Evaluate: lim x--2( 2x 2+5x-12

A: Topic = Limits

Q: 2x2 - 7x + 3 If f (x) = then lim f(x) will be X-3 %3D 5x2 - 12x – 9

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Q: Consider the following. 3x* - 8x3 + 9 = 0, [2, 3] (a) Explain how we know that the given equation…

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Q: 2x2 – 7x + 3 If f (x) = then lim f(x) will be X-3 %3D 5x2 - 12x - 9

A: We need to evaluate  limx→32x2-7x+35x2-12x-9If we substitute 3 in place of x directly, we get 00…

Q: V21. Show that there exist constants M and N such that M||x||| < ||||2< N ||x|| -

A: Given ||x||1=∑i=1n|xi|=|x1|+|x2|+...+|xn|       ||x||2=∑i=1n|xi|2=|x1|2+|x2|2+...+|xn|2 Now we have…

Q: Q1(i) Prove that Lim + a+ 1 2n²+1 V2n²+2 V2n²+n]

A: (1) Given, g(x)=limn→∞12n2+1+12n2+2+.....+12n2+n suppose any f(x) and g(x)…

Q: 16) what are the vertical asymptote(s) of f(x) = x+5x-6, %3D x² -1

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Q: lim 2V3. +onx 2cosx+1 %3D 6.

A: Our Aim is to evaluate limx→π623×tanx2 cosx+1 -(i)

Q: lim₂+-1 f(x) = C 2

A: limit exist when

Q: a) f(x)=-x- 13x²+3x – 9 Туре of polynomial Degree Sign of leading End behaviours Domain сoefficient

A: given that f(x)=-14x3-13x2+3x-9

Q: 3s Use the convolution theorem to find L-1{

A: