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

Q: Q5: prove 1) e2-j3n-e² = 2) |e²| = ex

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Q: 64(1-) Please explain in detail the step6) t from A to B Thanks, B = | 16(4 -JT) %3D

A: The objective is to explain the steps. Now, step A is, =641-π4

Q: v.(AX 8) - 8 ·/TXA) – A (vX 8) Prove the earuation.

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Q: 2. Assume that x > -1. Prove that (1+ x)" >1+ nx for n = 0, 1, 2, ....

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Q: Show that kT| e-t²/kTdt = (kT)3/2 " 0. 2

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Q: 222 – 7z (z – 1) (z – 3) - -

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Q: 3) FIND A PARTICULAR SOLUTION OF THE ODE y"+8y-20y = 2x +5 - e?X %3D

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Q: Oa, 1+ 16a, 2+ 225n for n> 2 with initial conditions ag = -23, a1 -19.

A: Given recurrance relation is  an=16an-2+225n     , n≥2 and initial conditions are a0=-23, a1=-19

Q: 11. If AJKL - AMKN, find the value of x. 12 N 20 x+1 Зх - 2 J

A: It is known that in a pair of similar triangles, the corresponding sides are proportional. It is…

Q: 15. Find x so that m || n. (5x – 20)°

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Q: f(1) = 3e " cosh (In 2r) -21

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Q: 22. Differentiate the following with respect to the variable x, giving your answer in a implified…

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Q: (b) Define fo = 0, f₁ = 1 and fn = fn-1 + fn-2 for n ≥2. Show that 3 fak for all k ≥ 0.

A: As per the guidelines we shall solve one question only as you have asked more than one different…

Q: 14. Given this diagram: 12 10 11 (a) What definition allows you to conclude that 410 is…

A: Given:

Q: Evaluate 6(4z² +10z+1)dz, where C is drawn in the figure 2i 2

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Q: 00 8tan-in Zn=1 n3D1 1+n2

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Q: 4. Prove that 3i² + i = n(n+ 1)?

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Q: 8²z 8. If z = x + y Inxy, show that x- 8 z + x² 8²z 8y² 8x8y

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Q: Suppose z = 5 + -2i and w -5+ -4i. Then Im(zw) =?

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Q: 7. 7. Suppose X - N(u.4), which is true?( X- (A) N(0.1): (B) PIX S0} = 4 (C) PIX-u>2; =1-0(1): (D)…

A: Here we use the properties of normal distribution to solve this problem.

Q: How do I calculate this? If Z~N(0,1), calculate Pr(1.55 < Z < 2.65)

A: Given that, Z~N(0,1)

Q: How can I calculate using Excel?   Suppose X~N(193,7), and Z~N(0,1). Then x = 204, is equivalent…

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Q: /2 5b) What is ll xl)=(2 ²) if x= G,s%2;X3=--) toce where -n/2 2. and Xn = L?

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Q: [2 1] Q2) Assume A = |1 3 L3 4] - anda-: [2 4 1 B = show that (AB)' = B' A' 13 6 4

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Q: Determine E მა მა + მო მა 2 - მ2 მ0 მგ if e8² = w sech 0.

A: The derivative of a function of a real variable measures the sensitivity to change of the function…

Q: 13. it BD AC DBE (2x-1. and mCBE (Sx-42) find the value of x

A: As per our guidelines we are suppose to solve only first question if the multiple questions are…

Q: 6. Show that =+ E-(-1)"(n+ 1) E)". when Iz – 2| < 2.

A: Seriese expansion

Q: (9xi – 3yj ㅠ S x² + y² + 7² = 9 is 2

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Q: -2t 7. f(1)=3e" cosh (In 2r) in two ways.

A:

Q: test if (AB)¹ = B¹A¹ A = 4 1 0 2 L3 5. B = 14 0 2 - -3 1

A: To test if ABt=BtAt.A=410235, B=14-3021

Q: 5s +1 To determine L-1. |s² – s – 12

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Q: A useful consequence of Taylor's theorem is that: |æ – c|" max|f(n+1)(2)| (n + 1)! > (æ)"y| (1)…

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Q: 1. (18pts) Find / simplify each: V100x*y7 + V54xy2 3 4 1 -2 2y5 2x4 205x V10x2 Rationalize * 3 1…

A: Simplify

Q: Simplify #28

A: The known fact is that

Q: of the indicated d 2. 17 in Z 4. 2x-3 in Z[x] 6. 2x -3 in Q[x] -8 2 10 in ZIr]

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Q: 11| Q1) If A--2 -1,B 3 3 4 -5 -1 -1 13 -1 Find (–1 x A) + (B + C)

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Q: H PROVE : กะ1 [-¹-², ¹+ ²] = [1,1] 1 t

A: As per our guidelines we are supposed to answer only one question at a time. Kindly repost other…

Q: find The Six Solutious of The eq- 6 Z+27+2

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Q: 2. Use a trig substitution to evaluate S dx x³√²-16' x> 4.

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Q: 3. 3r+ Sy - 2: = 52 4r+ 7y +a= SI -2r- 9y + Sa--53

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Q: e2a – 6e" – 27 = 0 - -

A: e2x - 6ex -27 = 0 here lets assume ex = y y2 -6y -27 = 0 y2 -9y +3y -27 = 0 y(y-9) +3(y-9) = 0 y+3 =…

Q: 2Fn>Fn+1 for n>3 true or false?

A: Given,       2Fn&gt;Fn+1 for n&gt;3

Q: 1. Find XY when X(-7, 10) and Y(3, 4).

A: GivenX≡-7, 10Y≡3, 4To find XY

Q: 18. y = x² + 9 and y = 10 + 2x over z = [-1,3]

A: The graph is shown below

Q: 6) Prove mathematically that (1 grad = 0.9 deg)

A: We know, that 1grad= 0.9 deg.  we can solve any other similar problem by multiply the number of…

Q: 1) y = a², from P(-1,,) to Q(1,;) .2 1 2) x = 3VI(y – 3), 1 <y<2 - 3

A: We have to find the arc length of given curve

Q: 3, 5x 60(x2 + *), 3 b) Y = In 7.

A:

Q: -25 (1+j2 Show that (3+j4 2- = 57 + j24 -j - 2

A: The expression to be proved is  -2521+j23+j4-2-j5-j=57+j24

Q: 16 3. Show that for x2 + 2xy - 3y² = 4, y" (x-3y)3

A: We will find y" as following.

Q: 3(xn)2+8 7 : If xo = -4, find x2 corrected to four %3D

A: