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Q: Let a, b be real numbers such that la], [b] >k> 0. Show that la - bl k² a ≤

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Q: Let M = {14*: kEZ*} and A = {7k:k € Z*}. Then

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Q: Fmid the value of k frs shich the has yoten 2x, + 4223k i Infimite 8luhen Ho

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Q: 3|n(n+ 1)(n+ 2), Vn E N

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Q: white and 3 blue ball wn successively with re wn in the order red, wn in the order white alls are…

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Q: S cscycoty 1+cacy dy Select one: OA. - In (1+ csc y) + C OB. In (1+ csc y) + C OC. In² (1+ csc y) +…

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Q: Evaluate d.x. 4(1+4) Select one: O ti - in 1+ a|+C 4 3 in |1+ z*|+C Ori- In 1+|+C 4 tai + In |1 + x…

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Q: Consider Check all that apply. OA. first order B. ODE C. PDE OD. linear O E. third order OF second…

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Q: 0 Let n be a real number and A = a. A is invertible for n # 0 b. A is singular for n = 5 c. A is…

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Q: Evaluate O O O O K|4 2 6 wo|= • S² +2²+1 dt. - 3

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A: The domain of the natural logarithm function "ln" is 0,∞. The range of the natural logarithm…

Q: 2 I=S -1 e cosxde

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Q: Show that for every real number s. 0 e- e-ste² dt = ∞

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Q: Let v=i-3j+k and w=i+j-k . Then (-3)||v-3w||:

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Q: Find the nth term for the following :function 24 25 23 32 4² 1 − (−1)n 2 n (2)" (n) 2,1, I I 52 B

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Q: 24. What is the simplified form of (-5x3y)2? 10, F. -10,8 Н. 25 G. -251 J.

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Q: Let à = − 3ỉ − 2j + 2k. Find ||ā||.

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A: For the given differential equation 4y''-4y'-3y=g(x) We need to find the form of a particular…

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Q: A. Evaluate the follow 1. S dy 3+√y+3

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Q: Compute. 13 Σκ k k = 0

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Q: Let E-fr.8.2): os es , 05 25 1,7√25 rs 7). Compute 6.8365-1051090 mit Answer x III. r

A: ∬∫Ey2 e(x2+y2)3= ∫0π∫01∫7z7(r sin θ)2. e(r2)3. r dr dz dθ= ∫0π∫01∫7z7(r3 sin2 θ). e(r6) dr dz dθNow,…

Q: 4 Let w = x. In(xy²z³), then which of the following is O a. 0 O b. O d. O e

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Q: Find Re (1+17i) 01 O-1 O None of the given O 17

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Q: find following timia the exist Pim 1t y ス→。 fim (2'tyo) In (xty?) ()

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.