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Q: Given that cos(x) = (-1x2 for e<xc than a powr saries of cas(x) %3D ie e (2n)!

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Q: If u = x² cosy+ ye", where x = s+2t and y = st, prove that ди ди 2- (s – 21) (x siny- xye – e"). -…

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Q: Evaluate the line integral (8x + 7y)dx + (2x - 7y)dy along the curve C: a = 8 cos t, y = 16 sin t (0…

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Q: in term of t, if w -+, x= cos t,y sint and z in term of t. if w = xy, x = cost and y = sint, whent=.…

A: 4. Given data is : w=xz+yz , x=cos2t , y=sin2t  and z=1t To express dwdt in terms of t

Q: 2. If z y where z= s cos t and y=s sin t, find az/ôs and az/at.

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Q: Solve the diferential egyatien dy - by Melne's méthool with h-o-1 e Cosx dx

A: GIVEN: y'=e-xcosx-y   The formula is: yn+1,p=yn-3+4h32yn-2'-yn-1'+2yn'    ............(1) Put n=3,…

Q: Show that Ě = 3xyê+G)+2Ê is R3 and Pind Conservative a potential Ø Rar F. on

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Q: 1₁ -1.2 - St 0 √x sin ex dx

A: Given :   I1=∫01.2xsinex3dx

Q: Compute Se (In(x + 5) – x²y) dx + (xy² + sin (e")) dy where C is the unit circle

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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: šiven r,(t)=sin5ti +cos 5tj+\t+2k and r,(t)=5ti+2k , calculate "[r, (0) •r, (0)]. dt

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Q: Evaluate the line integral / (7x + 5y)dx + (3x – 9y)dy along the - curve C: x =2 cos t, y = 4 sin t…

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Q: let Po)- tar'c) + tant (L). show that Plx)=C,where cis a constant and then Aind C

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Q: (t – sin t)v1 – cos t dt

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Q: Evaluate the line integral / (3x + 9y)dx + (4x – 5y)dy along the curve C : x = 10 cos t, y = 20 sin…

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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: iven that y = sin? (t) and x = cos ( 4t?), hence find dx dy a. 8t sin (8t) sin 2t 8t sin ( 8t2 ) b.…

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: please show all steps

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Q: show that the Punctionc Sinh t V3 and ye T5 Sinh t+ CoshE 13 taken together satisfy thediff erential…

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Q: Gren thint sin (A+i6) = xtiy, 28 Prove that, 9父+ =1 snh'B 1) x essec?A -y' sec'A =1

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Q: Evaluate the integral / (4 + + sin t)° cos t dt using the substitution u = 4 + sin t. (4+ sin t)°…

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

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Q: DIfferentiate the following fuh ction with respect to K In X %3D Sin a

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Q: a/ tangent s lope rasinczo) ) when e zT 9. 父 A dy do 2 517 dる 2. fhe D not of tne above

A: Given,  r=sin (2θ) Recall:  Slope, m=dydx

Q: sin(iny)dy is equal to * y (A none of these cos(ny) + C y cos(Iny) + C (D) -cos(iny) + с cos((ny) +…

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

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Q: Evaluate the line integral / (3x + 7y)dx + (2x – 3y)dy along the curve C: x = 6 cos t, y 12 sin t…

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Q: 3. Given that z= (u, v), where u 2r cos y and vz sin y. Find and Hence, show that Dy

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Q: (2823 у — 3D 252*у — 6 sin 3а) dx (20x°y3 – 21a*y?) dy 4.4 - -

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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: dy Find dt y = cos (V6t + 12) 1 O A. 2/6t + 12 sin (V6t + 12) O B. - sin (6t + 12 3 sin V6t + 12 Oc.…

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Q: 7. Calculate dy/dx at the point indicated: f(0) = (7tan O, cos O), 0=/4

A: Here we will use the concept of parametric equation and Derivative of parametric ewyations

Q: Let f(x, y) = 2e sin(4) of д х of dy Check Answer

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Q: Find ſ z2 sin z dz

A: We can find the integral in the following steps

Q: show that1) d/dz [cosz] = -sin z

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Q: If we have to check the DE (5-8y+4xy)dx = (x+2)'dy for Exact then My %3D

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Q: dz Let z=sinh -(y-2x), where x = we and y=In then is given by du

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Q: Evaluate the line integral ( 9х + 5у)da + (х — у)dy along the curve C : x = 6 cos t, y = 12 sin t…

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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: Q1\ Differentiate the following (c 1)2xsin-13x 2)y = In *+1 Vx-2 %3D 3)y %3D sin-1 2x

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Q: Evaluate the line integral / (2x + 7y)dx + (4x – 6y)dy along the curve C: = 6 cos t, y = 12 sin t…

A: Let's find.

Q: Evaluate the line integral (2x + 4y)dx + (3x – 9y)dy along the curve C : æ = 2 cos t, y = 4 sin t (0…

A: We need to evaluate integral.

Q: Find where) i ) et u*rany tany = 1 , U= xInx (use chatn reule ) ii) coscxy) - * + e+y) = 2 yz

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Q: 1. Differentiate F(t)= e4t° sin sin 2t [Hint: y = e", u = 4t³ sin 2t.]

A: In this question we have to solve the differentiation of the function.

Q: f : [o,s] → A? flt) = ( 6E) 2 cosh 3t, - 2 sin 3t, Compute f'lt).

A: If f(t) is differentiated with respect to t, then f'(t) is obtained. Let f(t)=x(t), y(t), z(t), then…

Q: (4) If z = f(r, y) where, a = e" cos v and y = e" sin v, show that (i) dz az e2u. (ii) az 2 2 dz -2u…

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Q: H.W. 1) Lt² sin wt 2)L t cos wt 3)L t² sin 4t 4) Lt³ cos wt .3

A: Recall the Laplace's Transformation, L{tnf(t)}=(-1)ndndsnL{f(t)} where L is LaplaceTherefore,…

Q: If we have to check the DE (5-8y+4xy)dx = (x+2)²dy for Exact then My

A: M dx + N dy =0