3. From the standard following two (2) pa a. Y= -4(x-9) ² Explanation b. Y= 2(x+6) + Explanation c. y = ½ x²-3 Explanation:

Q: B. 2(m+n)

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Q: 2. EIN 플 (sin³x)√1 + cos x dr

A: To Evaluate:   ∫π2πsin3x1+cos(x)Since we know that     sin2x  =  1-cos2x  = (1-cosx)(1+cosx)So,…

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A: Let F is a field, then we have to prove that F is division ring.

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Q: 14.Consider the group (A, *) where * is defined by the table below * A B C D AB A D с BA B C DC D C…

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Q: Evaluate the following integrals. 2. [** (sin³ x)√1 + cos x dx 플

A: It is known that ddxcosx=-sinx. It can be written that: ∫xndx=xn+1n+1+C.

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Q: II. Evaluate the following integrals. 3. √²|2 - 2º|dx 0

A: The given function is  y= |2-2x|  =2-2x   when 0≤x≤12x-2    when 1≤x≤3

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Q: Question 2 a) f₁(x) = x, f₂(x) = x-11 (3(x) = x+3 is linearly independent on the intral (-∞0,00).

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Q: Prove the following by using induction: 1(1!) + 2(2!) + 3(3!) +...... + n(n!) = (n + 1)! - 1, for n…

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A: Solution :

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A: Given,C1 : x2 +y2 =16 , C2 : 4-(x+2)2, and C3 : -4x-4

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Q: condition o

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A: The given area is enclosed by                         y2=x  and  y=x3

Q: [69] Q4)(a) Find the maximum eigen value for the system A = x (0)=(0.02991) with initial vector (5M)

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Q: 6 An advertisement bulletin board store has 1750 light bulbs. Each year, about 1/6 of them burn out.…

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Q: (4) Let A be a nonempty subset of a bounded set B. Why does inf A and sup A exist? Show that (a) inf…

A: let A be a nonempty subset of a bounded set B. why does infA and supA exists? show that  (a)…

Q: III. Consider the region R below bounded by the curves C₁: 2 - 4y = 4, C₂ y = √x-1, and C32 | 2y =…

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Q: 3.x+y+z=4 - x=y+z=-2 2x -y + 2z=2

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A: Given as, B= { 4, 1, 5, 3, 4, 3}

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Q: II. Evaluate the following integrals. 3 3. | 2 – 2ª | dx - Jo

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