Prove that: n² + 3n 1 →> 2n² + 1 2 You may use any results from lectures, but you must state them clearly.

Q: [ (ax + b) c+b) dx = ○ / (ax + b) ² + C O O4a ¹ª (ax + b) ² + C O4a (ax + b)² + C O4 (ax + b) + C 7a

A: You must have basic idea about indefinite integral in order to understand this better.

Q: Find r(t) and v(t) if a(t) = tk, v(0) = 15i, r(0) = 14j.

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Q: Show that if A × B = B × A then A = B

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Q: Find a x b, and c* (a x b) a = 2i + 3j - k, b= -1 + 4j + 5k, c = 2i + 3j + 4k Show all steps

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Q: Which of the following is equal to (2° – 7æ)*dx = (x6 -

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Q: Which expression(s) is (are) equivalent to 5 (x+9) + 7 (y + 2) – z? Select ALL that apply. O 5x +…

A: Answer is 4x+7y+59

Q: ƒ(5x² + 4x³ − 2x + 1)dx 이름 +2 -를 +a + C 5 2 O x5 x5 + x²-x²+x+C O 20x5 + A O 20x³ + 12x² −2+ C…

A: Given, ∫(5x4+4x3-2x+1)dx

Q: draw the solid x² + y² +2²=2 2 = √3x² + 3√²

A: Given equation are: x2+y2+z2=z z=3x2+3y2 To find graph the given functions.

Q: { :Find the first 3 terms for 2n-1 (2n-1)! (−1)n+¹

A: given sequence  -1n+1x2n-12n-1!

Q: acosa (x)+-5sin (x)-4-O

A: Consider the equation,

Q: 2ア+ 2z+ 11 (2ェ+3) (z +4)

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Q: Which of the following is equivalent to 3x²(-2x)e-x² + e-x²16x O -16xe-x²(x² - 1) O 16xe-x²(x² + 1)…

A: Given query is to simplify the expression.

Q: Suppose that |u xv = 7. Find ||(5u + 6v) × (3u - 9v)||-

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Q: 16 Evaluate x1² (x4 – 2x² + 1)²dx. - 81

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Q: n=2 n (2n — 1)!

A: The given expression is an infinite summation, where the indexing variable "n" starts from 2 and…

Q: [1 2 3] ii) Let A = 4 5 6 and B = 5 L78 5] L3 of C32? [-5-5 71 [C11 C12 C13 - 2 4. Suppose BA = |C21…

A: First we state the general formula for multiplication of two matrices and then solve this particular…

Q: 3 So² √(√₁² - ²√₁²³) ²³ a dt

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Q: 4x – 2 > 2(x + 6)

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Q: Find curl (82 i + 9x j + 6y k). curl (82 i + 9x j + 6y k) = = ( )k )i + (i )j + (

A: To Find : curl(8z i + 9x j +6y k)

Q: For which value of b is the equation 2n+1 11 5n+1 10 satisfied, n=1 where b>2 ? (a) b=3 (b) b=4 (c)…

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Q: 00 (2n +1)" n2n n=1

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Q: given 7(x-1)=2(3x+2) prove x=11

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Q: Can you please revisit 2 (b) , I think it is not correct , especially an+1.

A: Let ∑an(z−a)n be apower series.Then the radius of convergence R=1limn→∞|an+1an| if limit…

Q: either find the following or show they don’t exist.  (a) 2A − B (b) A + 3C (c) 2A − 3Ct

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Q: E[2A+ 3B + C – E + 2D] |

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Q: Find the 7th term of 2+ 2 Write the 5th term of (x + y)1º.

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Q: 5) Find CD 2x +21 C D x + 21 10

A: Given the line segments

Q: (z+1)(z+6)(z+10) z(z+2)(z+3) 3. What is the residue of at z = -2 (z+3)(z–2)² (z+2)(z+6) 4. What is…

A: 3) Given f(z) = (z+1)(z+6)(z+10)z(z+2)(z+3) Then Res(z=-2) = limz→-2(z-(-2))f(z)= limz→-2(z+2)f(z)=…

Q: Evaluate using the substitution method. √ dz 2x4 (6 +x5) 4 2 1 [(26²du) - 15 (6+23)² + = = + C +x5)³…

A: Given ∫2x46+x54dx

Q: 9. Find the quotient and the remainder of x³ + 2x² – 1 divided by 3x2 +1 in Z7[x].

A: Note that for Z_7  Any number is equal to the remainder when it is divided by 7.

Q: a) 1 (x-1)(x+2)(x+4)

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Q: What is a simpler form of 5n(3n3-n2 + 8)?

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Q: 13D 43. If a > 1 and b < 0, then 1-101 (A) (B) 1 9 (a) (D) b(a+1) (E)

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Q: 3x-11 mang má O a. Inkx+6Xx-17+c O b. In x-1)(x+67+c Ocinkx+1Xx-6+c Od. Inx-6)(x+1)+c

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Q: A D 15. Simplify. (2 – 5) (42² – 2z + 1) 4x³ – 22z² + 11z – 5 O 423 + 22z² + 1lz +5 O 4x + 22a² +…

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