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Q: If sinr = In y, show that dyOUTM dr OUTMO (1--- (1– 2) dy = y. dr

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Q: Date Page 28 uhore Jyln) psthe Bessel's fuction of the first kinf- uf onder Ur

A: To show: The identity, ∫Jv+1xdx=∫Jv-1xdx-2Jvxdx, where Jvx is the Bessel's function of the first…

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Q: 7. Evaluate. LL sin z da dy.

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Q: 3 Find C at any time7 2l/min SIN SIO 6l /min 8 elmin C NI8 100 Pure waley

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Q: (a) The averages of cos x and lcos x| from 0 to x are (b) The average of the numbers v,, the average…

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Q: 19 · sin 0 = 5 -4 7t 7n 11n B) {", Ila, 6. 6.

A: Given that, -4 - 25 · sin θ = -19    5   - 25 · sin θ=-19    5 +4-25 · sinθ=-19+205sin θ=15·-52sin…

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A: Given,           ∫0πax+bcosxdx=6To find: The value of a.

Q: (1+cot 6) de 5. sin' O14 - cote let, u= du=

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Q: Dipsonsiyel Dentlemler Sinay Asagıdati birinci drece difransiyel Denk- y/1) - T kosulunu seğlayn…

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Q: 1.tr Y= 4 In ( In (In(sec(x)) then Y 14 (lan)! In ((In (sec)) In (sex);| O True O False

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Q: 2- Find the solution of the diff. equ. dy ty Six dx

A: First Order differential equation :        Consider the differential equation…

Q: y = 46 tan B3 – 2 = 4¢ tan az – 2 %3D and y = 46 tan B2 +2 = 46 tan æ3 + 2 %3D and hence all the gas…

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Q: 1 Suppose y = tan ¹æ. Then x = y tan Otan y Oarctan y

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Q: dy If tan(ry) + 5 = ry then show that dr? 2y

A: Differentiation two times

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Q: 4 cos z Evaluate S 16-y2 ydxdydz

A: To solve the given triple integral ∫0π∫04cosz∫016−y2ydxdydz…

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Q: ome If y tanx, prove that y"-2(y +1)(3y+1). ir If x= sect and an

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Q: 1on to ove tha (X +Y)(X + Y) =X

A: In this question, the concept of Boolean Algebra is applied. Boolean Algebra A boolean expression is…

Q: (6) Euter eio_ el" = Cos e +i Sino, whore i = J1. where i= JT,

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Q: EX. Apply 4th order Runge - Kutto to s olve the toll Valu e Problem 4'= 44 for hzoid , y(1) =1. and…

A: Given diffrential equation is, y'=x2+y having h=0.1, y1=1 and 1≤x≤2 Now,…

Q: 27) tantt Cost =Gect 30) - #sint Cost Hant t sect 33) secx cscx = sečx+ cst^X. 36) cs COSX shx…

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Q: O if Z= x'tan!Y final dž Handwriting Point Cl,!) In

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Q: s show that: sinhCA+B) = SinhA. cush B + Cosh A. simhB

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Q: 15) y' = y tan(2x), y(0) = 2 16) (x+1)y' = 2 y, y(0) = 1 17) 2.xy' = 3 y, y(1) = 4 18) y'x In(x) =…

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Q: 3 Evaluate the gwen tri ple in legral. xsiny dy dz dx

A: Order of triple integral dydzdx

Q: 4. sin M= 20 16 30 5. tan L = 6. cos Z = 16

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Q: Sỗ ſcos ur sin u dr du 0 0

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Q: 7. If p(z) cos z, find y(0), p*), p(x), p(-z), p(r – y) %3D

A: Topic - value of trigonometric Function

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A: 11) From 0 to 5 there is a trapezium and from 5 to 6 there is a triangle

Q: 22: Evaluate Sea s cos²(y s) ds.

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Q: (a) If u(x, y) = cos-1*" + y* ) x² + y? = COS then prove that ди du + y = -2cotu

A: Given: ux,y=cos-1x4+y4x2+y2

Q: 21. xª sen z dz -z' cos z + 3z² sen z + 6z cos z 6 sen z + C %3D

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Q: 10. Prove the following formulas: du cot u %3D-сsc и. 2. а ) a dx d dx du csc u = - csc u.cot u. b)…

A: (a) ddxcot u=dducos usin u·dudx=dducos u×sin u-cos u×ddusin usin2 u·dudx=-sin u×sin u-cos u×cos…

Q: Suppose you Know that tand 3/12. Vsing this infe, de tevmine cuhot quadiantdis in dnd Caliulate…

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Q: 10- If f(u, v, w) is differentiable and u = x - y, v = y - z, and w = z - x, show that fe fe fe = 0.…

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Q: S(32+2*)sin(z)dz 3z +

A: In this question we have to solve Integration.

Q: Suppose the true relationship of Y and X, Z is given by 1. Yi = B1Xi + B2Zi + ei under classical…

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Q: If z = exy where x = In(u + v) and y = sin(u-v), find az and az du

A: We use the partial derivatives and chain rule of differentiation to answer the given question.

Q: .2π π 1 -εrocos? θ r dr sinθdθ φdφ x 32 πο X = ?

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Q: 10. If e is the acute angle between the surfaces xyz = 3x + and 3x - y + 2z = 1 at the point (1 -2…

A: We have to solve given problem:

Q: 26. /(х, у) — х 27. f(х, у) — sin y 28. /(х, у) — х1 + 9у2

A: fx,y=x fx,y=siny fx,y=x2+9y2

Q: 16 Find Ehe eract length of Ene eurve, /2 x= e- 4E, y= Re O<6< 2

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Q: 15 Iţ coser (Kt@)+xQse COHT) then x= - Sane cote f) care

A: The given equation is: cosec π2+θ+x cos θcotπ2-θ=sin π2+θ To solve for x. Use cosec π2+θ=sec…