OL. If w = f(u, v), u = cosx and v = sinx, show that: (30 Marks) %3D d?w dr v² fau + u?f- 2uvfuv - ufu-vf,

Q: дz əs дz at || 11 z = e cos(8), r = st, 8 8 = √ S6 + 56

A: Solution is done in step 2,3

Q: Ex:57 Find the FisiE of the Juuctiou sin TIt ZL oくtくし - siu -Lくtく

A: Given, The formula for the Fourier series expansion is,

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: P(T) = %3D P(T|R) %3D P(RIT) = %3D P(T and D) = %3D

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Q: If z = f(x, y), where x = r cos 0 and y = r sin 0, show that a²z 1 a°z 1 əz r дr дх? dy? дr?

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Q: Let y = (sin z+ cos r)e", x E [0, 27]. %3D

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Q: If y = tan u, u = v - and v = In x, what is the value of y at x = e? dx sec? e 1 O Option 4 O Option…

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Q: In AXYZ with a right angle at Y, the cosine ratio can be used to find the length of XZ as O a) XY…

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Q: Find a suitable A and B so that: A < S, Vx+4 dx < B

A: The given integral is ∫29x+4dx First evaluate the integral as follows.…

Q: angleO: Find a Tayler saries for Hhe Sunction fa)= In G) contered at a=I

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Q: Q.3 Show that Je dx=r

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Q: Find the general antiderivative. If the substitution method is used, state first u, du and [lu)du.…

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Q: Given f(x, y) = 6e sin(2y) %3D Question Help: OVideo

A: We need to find del function at given points.

Q: If u = x¹y + y²z³, where x = rse, y = rs²e-t and z = r²s sint, find the value of Ou/Os and Əu/ər…

A: According to the guidelines, we are answering first question. Please repost the remaining.…

Q: where yco,t) = y (5,t) = = 2Jx2 and y cx, o) y (X,o) = 10 sin 4T X

A: We solve the differential equation by the method of saperation of variable. In this method we…

Q: If PQ = 9 and QR = 28, find PR. %3D %3D

A: We use  formula to find PR. PR=PQ+QR

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

A: Differentiation two times

Q: Given y = sin u and u = 3x + 1, find %3D %3D 9.

A: We have to solve the derivative

Q: Be w = (u2 + v2)3/2, where u = e-t sin(θ), v = e-t cos(θ), calculate: ∂w/∂t and ∂w/∂θ

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Q: Use Green's Theorem to evaluate |(3ye2* – 7 sin? (3x* )) dx +(5x* +2x’y² +8e*-1y+2 where C is the…

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Q: U is y= cosx. A

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

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Q: Find d cos Z dz

A: Use the properties of differentiation and the derivative formula ddxeax=aeax, to calculate ddzcosz,…

Q: Q.2) Evaluate Cos(z + y+2) dzdydz

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

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Q: Given f(x,y,z) = sin (2xy) + 5xyz3. Find fyzy(3,2,4).

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Q: Given f(x, y) = 3x* cos (y), find COS fzy(x, y) = fyw (#, y) = | %3D

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Q: ind a suitable A and B so that: A< S, Vx + 4 dx < B

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Q: The reverse order of f, S, sin y² dydx is f, S sin y? dxdy False True

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Q: 01. If w f(u, v), u = cosx and v = sinx, show that: d'w dx2 = v? fuu + u? frv - 2uvfur - ufu - vf,

A: Given w=f(u,v), u=cos x and v=sin xso we see that dudx=-sin x =-v   and dvdx=cos x=u.By chain rule,…

Q: The þaramehc equalion of the unde x+ =9 is ☺ x = 9 cost, y=9 sint X = 3 cost, y= 3sint X = 3 cost,…

A: A circle is a two dimensional  shape an it is  a closed curve . A set of all the point are at the…

Q: Find ∂w/∂r and ∂w/∂s when r = π and s = 0 if w = sin (2x - y), x = r + sin s, y = rs.

A: Given w = sin (2x - y), x = r + sin s, y = rs

Q: EXpress ume trig fatIOS as TTACCTIOTIS TII Smmpiest teTIIS. 16 R. V33 17 sin R = Cos S sin R and cos…

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Q: Find fr(x, y) and f,(x, y) given f(r, y) = tan r - cos(r² – y³).

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Q: fro assoc е топоwing probat df = 8, P(t 2 2.306) give degr с. df%3D21, Р(—1.323 <1< 3.1

A: We are authorised to answer three subparts at a time since you have not mentioned which part you are…

Q: Q12) If w=f(a,b,c)=cos(ab)sin(b)+c, what is at ( -,6 )?

A: Given ,fa,b,c=Cos abSin b+CPut 12,π3,6i.ea=12 ; b=π3 ; C=6

Q: g(x) = Af(Bx), where: %3D A = %3D B =

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Q: nd the work done for the fo om (1,0,-2) to (4,6,3).

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

Q: If sint = - - and t is in the 3rd quadrant, then tan t %3D V45 45 O V45 V45 2 V53 O O O

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Q: Let glt) =e"t + Ž G ). sinCnt) Slre y'+4y=gGt),( deare the anouerr こ as a pariès.)

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Q: If y = tan u, u = v - and v = In x, what is the value of at x = e? dx sec?e 1 O Option 4 O Option 3…

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Q: Given f(x, y) = 7æ° cos (y*), find .9 COS fzy(x, y) = fyy (x, y) = %3D

A: Given  f(x, y) = 7x9 cos(y8) To find fxy, fyy

Q: dy _ 2y 4. If tan(ry) + 5= ry then show that dr?

A: We have to do differentiate with respect to x.

Q: The colution oF y" + 16 y = 0 is y= C,cos 4x + C2 6in 4x. IF y C0) = 8 and y' (T/4) - 32, find…

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Q: dy let y = (z sin z)² then is da

A: SINCE YOU HAVE ASKED MULTIPLE QUESTIONS IN SINGLE REQUEST, WE WILL BE ANSWERING ONLY THE FIRST…

Q: Evaluate F· dr C where F(х, у) %3D хуі + уј C:r(t) = 4 costi+ 4 sin t and 0 <t<.

A: Given that , Fx,y=xy , yrt=4cost , 4sint and 0≤t≤π2 Evaluate ∫CF.dr=?

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: Ex Find the Salution of the sliff. equ. + 2x° cosx, given that yf z dx

A: Here we have to solve differential equation