- Emluste ihe given limt ké", ut, 177 2. Compute 1he dovivadv'e A she given vactor hu. F()- くl。()tう4) eueluate the given Intagral 3 - Sr) whore Lt) -t- 2t ジ+ Co(36)に It

Q: 3. Evaluate || (3y+ 2x“) dA, where R = {(x, y) E R² : |x|+|y| < 1}. R.

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Q: 20. Use u substitution to evaluate. S secrtant 1+secx dx

A: Evaluation of the indefinite integral by substitution method

Q: 7. (a) V.(V4) = V²¢ (b) (4× R) _ (2-n).A n(A.R)R %3D E,r =|R|

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Q: QUESTION 5 3-1 The valun uf s of fox)- in the interval (1,0 such that f- 31-N) OA 3 OB. 3. В. OC 3…

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Q: 10. If O is the origin then the dilation Do, 2:(3. – 2) –→ (2, _?_).

A: DO, 2 means dilation of 2 about the origin O.  So the coordinate will multiply by 2. 2×(3, -2)=(6,…

Q: Verify that ) Determine from y Graph the solition of the IVP. is a solution of the ODE. . the…

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Q: Ex: © Suppise that the fiowing Aransferuntin Conneclğs the lei) and (ti) coordnate Syshems; a4ス?) 2…

A: Given that, ζ=x¯1=ex1+x2x¯2=ex1-x2 To find: a) Jacobian matrix J and J-1 b) Compute J¯

Q: ²*6²²y dy) dr 3

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Q: x° 25°

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Q: . Eualuati losh (12)d2 uhere. C di the Ciscube. lel=2

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Q: 18. а, 3 3+ (-1)"

A: This question is related to series and sequence.

Q: 2) y' – 10y + 25y 24te y(0) = –2, -10; - = (0)fi

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Q: 21. tant u du 3 tan u — и + С

A: Consider the following equation:

Q: ['yes' dy. Ans. (1 - ¹).

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Q: -6 B) [ x In(x) 12

A: First I have used the property of logrithmic and made the integral easy and then by substitution…

Q: 5. Let F= [3,2,1] and r= [2,1,–3]. Compute the following: %3D a) Proj „F. b) Orth rF = F – Proj „F.…

A: We know that  ProjrF=r.F∥r∥2r Now, r.F=23+12-31=5 ∥r∥2=r,r        =2,1,-3,2,1,-3        =22+11-3-3…

Q: Frod the averuge vearlue of the durndkam f over Shoe lad eraual [q,9]

A: Given function is fx=9x3. Need to find the average of f on -9,9. The average of the function f on…

Q: Given preimage AQLU. T(X, y)x-4, y-3) to find AQ'L'U'

A: We have to find the coordinates of new triangle

Q: 33) In quadrilateral RSTU, Es I ST and ŪT I diasgned If RS =6,ST = 8, and 12U = 15, find UT %3D

A: We can easily solve this problem by using Pythagoras Theorem in both the triangles (one by one).

Q: dy de Xoy. -Secxy)

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Q: 5) What is the maximum value of y = 5 Cos 4x ?

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Q: 2 a) y = Find y'. 3e (ax-5)4

A: Explanation and solutions is given below.....

Q: Linerje the mon- liven ie the rgin *T/タテノ

A: Given: A non-linear equation, z=x2+xy+3y2 We have to linearize this equation in the region, 2≤x≤3…

Q: D.4) show that is boundled) abng the if I sinz line&CXoy):dX-By =of Straight then

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Q: obtan al the real solutons af 4sinhte 4onh 42 -17 sinh3x + 4 sinhzz =0

A: Note that x=0 is a solution of 4sinh4x-17sinh3x+4sinh2x=0.

Q: Find yp for y" + 5y' + 4y = -2x + 3 1- O Option 1 XIN 2 +8+ C

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Q: 19) fiud eq uilibrium Point for the demond arol Supplie fumetion of Dq = - 1.259+ 475 and S) =…

A: Given D(q) = -1. 25q + 475 S(q) = -1. 125q + 266 For Equilibrium, D(q) = S(q)  0.125q = 209 q = 1672

Q: 2. K42

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 2. Find the siope of a ine witi tie given points (-Z, -9), (ū, -5), (Z, -i), (4, 3)

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Q: S dx 4+e*

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Q: Let S(の= メー4x + 3 a> find The wer texc o Describe The end behavier ondgraph c) Find woe fie inc reas…

A: "Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: sLI) =10 Soloution is 8=?

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Q: Hnd the generalsolutm to y" f4y'+13y =O Ganerat Soluhon:

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Q: (1) Lin Ⓒ (-215) Irccd.instructure.com/courses/187394/assignments/4737343?module_item_id=14431338…

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Q: 1 du = u - In(1+ e") + C to evaluate Use the fact that 1+ eu dx. I+ ex3

A: Given

Q: 3)으 rcose de Jsine 1-x2 d ¿= xp 2

A: LEIBNIZ RULE