So Simz So e" dz dy dx uate: e + Vē – 1

Q: dy sec (re ), y(In 4) = 3 / t dt

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Q: Prove that when y = e 2 Sin 2.x, then 4- d y dy +17y=0 +4. dx? dx

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Q: S (x, y) = sen (r² – 0²) + In(r® + 0), con Vr? + y? A r = = arctan

A: Given that, f(x, y)=sen2r2-θ2+lnrθ+θfor r=x2+y2and θ=arctanyx

Q: Iffis of class c? and z= f(y.x), con u= x°y°,v = 5x+1. Verify that| :4xy kxy+ 4x³y° + 10xy- af дхду…

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Q: 8.If V=k r°, and V=4 when r=2 if dr/dt =2, find dV/dt ind th

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Q: Evaluate: S (In(2æ – 1) – (5) + 25 ) dx - Limits: [1, 6] Using Trapezoidal, n = 30

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Q: 0. gy c ube a losed Cont Conlainig he okigin it. Pycoue thal az 2.

A: I have used Cauchy integral formula

Q: Delermine seich all mateuraal neumbers e, y 4 that ayz t scy t Iz tyz tety +złl=2020

A: You must have an idea how to do factor of any equation. The

Q: If z = cos (r + cos y), show that az Fz ar ərðy dy dr

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Q: If u=x2y+y2z+z2x then show that du/dx + du/dy + du/dz = (x+y+z)2

A: Given u=x2y+y2z+z2x. Find dudx as follows.…

Q: J. In (T/2) cos ey dx dy In (/6)

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Q: O! Find tue indefinite integrel by q meleing tue febstelion d=4 Sin o. 2 *7 16-x"

A: To determine: by substituting x = 4sinθ

Q: - Evaluate the follwoing | r" exp(ax")dx where a + 0 and m+l = 1, 2, 3, ...

A: Given integral is, ∫xmeaxndx Substitute, u=am+1nxm+1dudx=m+1am+1nxm+1dx=1m+1am+1nxm+1du Then,…

Q: 6. Prove that ſex*dx+rydy = Sc r*dx+xydy+Sc, r*dx+xydy+Sc, x*dx+ rydy.

A: Prove that: Where c is the curve of the integral. The curve c is divided into piecewise region.…

Q: 25-x² dx In if we let u = V25 – x , then udu =-xdx.

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Q: In r dy If y , then is cosh z

A: Straightway proceed to differentiate both sides,

Q: if y= Cot" (-+) y=Cot Prove that dy 1-x

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Q: Evaluate (2х — у) dx + (х + 3у) dy. C: elliptic path x = 4sin(t), y = 3cos(t), from (0, 3) to (4, 0)

A: Line integral

Q: d - [sin(t) dt = 0, Where k is cons tan t dx Select one: True False x

A: Here, the integral has the constant limits 0 and k. So, ∫0ksin(t)dt s in terms of k that is…

Q: Find the general soulution dy/dx=3y

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Q: 8:54 1 3. If y = (5x)sin(3x) , then %3D dy %3D dx Type here to search

A: This question is related to differentiations. Solve in 2nd step.

Q: -2 -In x SLy e dz dx dy O 7/24 O 7/48 O 5/48 O 47/24

A: We have to find the integral.

Q: dy 3) Determine the of : In (ху?) %3D х у dx

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Q: Lind dy/dx O ztanag In 3 Funas Inx I + Inx

A: Consider the provided question, We need to find  dydx of the given function. (1) Given,…

Q: dy IS let y = (cos r)m " then de sin z

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Q: Find dy dx? A) y = 3sin u - sin'u and x 3 cos u- cos'u

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

Q: Te 2=tnx then prove thot dx 28 Snメー tty? 1+xて

A: We have to use proper calculus applications.

Q: If y =Aex +Be™ d'y -(m+n) dy. Show that + mny = 0 dx

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Q: 3. If z = f (x, y), where x = e“ – e® and y = e® – e", show that UTM UTM az az UTM X : az - ду dx…

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

A: Order of triple integral dydzdx

Q: Ex 15: Prove that : d du a) tanh u = sech² u dx dx

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Q: 1. Obtain the par hicul ar foluhon 4 DE . 9xy dy a. oy dx = ; uh en x= 2,y=1 b. 4xy dy = 2y (I+ y?)…

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Q: inlyralf Evaluste the +2) ě Snz.dz whre CiI21= 1, by any tw o methode and compone the resalt.

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Q: dy 3 (113) _1) dri Ber roullis Solve this by using caruation. %3D

A: The equation is given by: dydx=31313-1 Assume x=1,y=3 to get: dydx=yxy13-xdydx+xy=xy14 Which is a…

Q: - 403 y = cos dy %3D de

A: Given : y = cose-4θ3

Q: 4. Use Green's Theorem to evaluate | ay dx + (1 – ry) dy where C is shown below y (14) F1,2), (1.1)…

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Q: Evaluate: / (In(2r – 1) – () + 25) da + 25 ) dx | Limits: [1, 6] Using Trapezoidal, n = 30

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Q: -41 sin tZ dz, c: 1Z-il=2 z4 ans: 3. coshz dz ,C: IZ1=1 27T ans :

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Q: If z=x+iy=r(cos(0) + isin(e))then

A: The given equation is z=x+iy=rcosθ+isinθ.

Q: In(v¤) dædy 6. 15. Calculate ry

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Q: find: Seos nit dt findo S sinnat at

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Q: ne exact length of tne X = Vy (y – 3), 4sys9

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Q: when y and u are defined as follows. y = 3u2 + 7   and   u = x2 + 9

A: Here I am attaching image so that you understand each and every step.

Q: (5) Under what Conditions is (ax+by) dx + (KX+LY)dy=o exact? selve the eXact equation,Ca, b,k, L…

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Q: Evaluate xy dS. S: z = 3 – x – y, first octant

A: Given query is to find the double integral in first octane.

Q: 1 +y = zy" dy dr

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Q: l? sc tue suell metuozd to fired tue voune of te Solid genented the by rerolning the plene rgim…

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Q: If y = tanu, u =v--, and v= In x, dy at x= e? what is the value of dx

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