B. Find the antiderivatives of the following. 1. ftáz 11. 4 sin z [-1) dz fco (2 +) dz. 2. 12. coS z 3. 13. dr - cos? z dr tan? r dr 4. 14. [Vī dz 5. 15. 6. 27+4dx 7. 8. xp- 7x 9. dr 92z + 4x2 10. dr

Q: dw If w = x'y sinz - 3zexy, find dz O a. dw =x?y cosz - exy dz %3D O b. dw =2x2y cosz -exy dz Oc. dw…

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Q: 37. ; with r = 1 andh = ;: 0, p2 sin¬! V1-h² /r²-h/r2-n? (0,, 33 47-3/3 (0, 0.71)

A: Let's simplify in steps Let's take the numerator first:

Q: Q. If z = f(x, y), where x = u cos 0 – v sin 0 and y = u sin 0 + v cos 0, with 0 a constant, show…

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Q: Q:Ifx = sin 6, y = 0,y= cos p6, prove that (1-x )y, xy,+ p°y= 0, dy and y1 d dy where y, %3! %3! de

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Q: EVALUATE USING HALF-ANGLE SUBSTITUTION dx 5 + 4 sin a A. aretan (Stan (3=) + 4 arctan +C 3 В. 2 5…

A: This question is based on indefinite integral.

Q: (d) Re(cosh z) = cosh x cos y, Im(cosh z) = sinh a sin y. (e) | sin z|? = sin² x + sinh? y, (f) |…

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Q: O(y-+ rycota)dr + zdy O (coszcosy– cotz)dr sinrsinydy 0 O ydr + (3z -g')dy = 0

A: A differential equation is called linear if 1) every dependent variable and derivative involved…

Q: If f(z, y, z) = sin(z) +ay2-23 then the value of a that makes div(Vf) = -sin(z) - 6z is Answer

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Q: 2. Given that z and w are independent variable and dependent variablerespectively, obtain dz/dw a.…

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Q: s gluai 2 si x = vt +1 ou y = 2xcosx + tanx? as il l J mal (x sec?x? + cosx – x sinx) (1 VE+1 1 (x…

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Q: (2) Use appropriate substitution to solve the following 1-1-y dy (i) dr tan (x+ v). (ii) y = %3D z+y…

A: As per our guideline we are supposed to answer only one asked question with first three subparts.…

Q: Consider y(5) + y" = 1+ cos( – t). Then a suit- able form of the particular solution can be written…

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Q: Consider y@) + y" = 1+ cos( - t) Then a suit- able form of the particular solution can be written as…

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Q: 3. Find an equation of the form y = ab* +c sin x) that fits the data below x01 2 3 y 4 11| 16 29 A.…

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Q: Again differentiate with sespect do 'x get we A cost- B Sinz A cosz + BSiny) { from @ d +

A: Please refer the attached image for complete solution.

Q: There exists a solution, F(x,y)=Dc, to (2- 2aye) da – (2ye + 3 sin y) dy = 0 such that - OF 2ye 3…

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Q: Evaluate: sin ycos ydy. sinºy A siny +C 8. 6. sin y sinsy + C 8. sin°y sin'y + C 8. - 6. sin'y + C…

A: Here we need to solve the given integral .

Q: 2. It Z = e tanly) , wnere x = S"+ t and y=St, find 22 when S=1 and t =0 2t

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Q: Solve the following DEs by LT. 1. y" + 2y' – 3y = sin(2x), y(0) = y'(0) = 0 2. y"" – 3y" + 3y' – y =…

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Q: [AFE] Given, f (x, y) : sin (x?y – 2x +4). Find fæ. O(-2xy+2) cos (x²y – 2x + 4) О 2гу - 2) сos (z*у…

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Q: S sin³x /cosxdæ =? O a. ( ?cos'z – cosz) vcosa + C O b. ) +c rt), O d. (cosr + cosz ) /cosz + C C.

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Q: If r(x) = -cos (x + 9) +7, determine the antiderivative of r(x). (Do not include the constant C'in…

A: In this question, we want to find the antiderivative of the given function r(x).

Q: 6. SS dV に lies b/w ミ 25 %3D and x? f y? + z? Ź 36 in the firót oct ant ...

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Q: u=x? +y² +=?, x=e" cos 2t, y =e" 2t, ==e = =? ôt e“ (sin? 21 – 2 sin 21 +41 +16r +2) Ob. e“ (cos 21…

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Q: 3. Find an equation of the form y = ab* + c sin (“x) that fits the data below x | 0 1 | 2 |y | 4 |…

A: To find the equation of the form y=abx+csin(π2x) which fits the data  x0123y4111629

Q: Find the following antiderivatives. 49 – 24 dy 44 +1 (a) / : (b) / tan u + tan u du Vtan? u – 2

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Q: Which of the following is the antiderivative of S 3 tan (x) dx ? a. 3 In In |sec sec x |+ 3x + C c.…

A: Given :  ∫ 3tan(x) dx   NOTE : To find an antiderivative for a function f, we can often reverse the…

Q: 1. If Z = sin r+ 2 I+1 6. - ", find dZ/dr.

A: differentiate with respect to x

Q: Answer True or False II| f (x, y, z)dædydz = ||| f (p.cos Y sin 0, psin y sin 0, pcos 0)p² sin…

A: To solve the given triple integral problem.

Q: If f(z, y) = e sin 8y, then fzy is given by: O 16 e sin 8y 16 e sin 8y O 16 e cos 8y 27 16 e cos 8y

A: We can solve it by taking partial derivative of both side two times as below

Q: Given that r = 3 cos nt, y = 3 sin at and z 4nt with 0<t <1. Evaluate (x+ 2) ds.

A: The line integral is defined as,

Q: 23. sin r cos? "x dr ².

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Q: 16.Which of the following is equal to fee dt ? O A. eet + C ee +C в. ee x + C D. ee 17.Which of the…

A: 16.∫eedt=ee∫dt=eet+coption A is correct.

Q: The antiderivative of Cos(3x) is Blank 1 (use small letter no space)

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Q: The general solution for the Euler DEx?v+y=D0,x> 0, is given by Ody= Cx/2. + C2xInx. O e. None of…

A: We will find out the required solution.

Q: 1) Given x = Vu2 + E2 sin 0 cos 2 y = yu? + E² sin 0 sin 1 z = u cos 0 ds? = dx2 + dy2 + dz2 %3D…

A: Hi! As per norms, we will be answering only the first question. If you need an answer to others then…

Q: | Calculate the following antiderivatives: / 6r – 2° + 7 dt = [T (a) +C. (b) ul/4 1 + 6yū du = +C. 1…

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

Q: y" – 8 y/ + 16 y = e²" sin 4z + 2e" + 5x sabit katsayılı homojen olmayan (sağ taraflı) diferansiyel…

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Q: ie LAPIACE nstorm OT 1. f(t) = e-5t cosh(6t) – (9t)"/2 2. f(t) = t³ cos(5t) + cos(2at) cos (3at)

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Q: dz az If z = xyeX/Y, x = r cos(0), and y = r sin(0), find and ar when r = 2 and 0 = %3D az ar (r, 0)…

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Q: (2? + y? + 1) dæ – (æy+ y)dy= 0 - %3D x +1 (x + 1)? Option 1 Option 2 (x + 1)-3 (x + 1)-1 O Option 3…

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Q: d the val 5) y= 2cos 30 6) y= 4sin 20 cos 0 7) cot F 7) y= sin (0-45) 8) y = 2 + cos 0 9) y= 3sin…

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Q: 1 Sa dy secy tany S sin ²x cos²x dx 2. S

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Q: Which one of the following equals (x + y) dx dy. 7/4 csc e Luh r*(cos 0 + sin 0) dr dð А. 37/4 Jo…

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Q: A) Let w = 4x2 +4y² + z?, x = p sin o cos e, y = p sin o sin 0, z = pcos o. Find aw/ap, aw/a6, and…

A: "Since you asked multiple questions we will solve the first question for you. To get any specific…

Q: fe and dr af Consider f(x, Y, z) = x² + y²z² and r = rsin 0, y = r cos 0, z = Or³. Find

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Q: Suppose y = y(x). Which of the following is ( +cos(ry) + 1) = 0 Select one: a y(y? sin(ry)– 1)dr +…

A: Take the derivative of each terms and arrange them in the form of given options.

Q: 1. Find the following antiderivatives. 4 - 2" dy 49+1 (1) / (b) / tan u + tan u du tan? u – 2

A: According to our guidelines we can answer only one question and rest can be reposted.