2. If z = tan(xy)+ 2 In(x+ y) show z, = Z = Z "хуу уху уух

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Q: 2ーてスース+スニ。 A ind yh ans: スi:z )スてニリ人3:)

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Q: 6. Y 12 12 9. 15 15 X. sin (Z) cos(Z) %3D tan(Z)

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Q: (A y = tan z B y = tan 1z

A: We have to find out

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A: Differentiation two times

Q: If y = tanh"(k/x) and x (1 - 144x) y'=A Then A= .

A: First we find the derivative of the given function y.  After that we substitute k=12 in the result…

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Q: dz and du dz Find when u = In 2, v = 1, if z = 10 tan'x, and x= e" + In v. -

A: Here we the chain rule to get the answer .

Q: lAcOs3x+B sin sx) この

A: Given solution with condition is  yx=exAcos3x+Bsin3xy(0)=0y'(0)=1

Q: (x cos + y sin?)y – (vsin? -x cos?)* х — х COS = 0 Ans: xy cos = c (Lucknow, 1997; Kanpur, 1996)

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Q: rcosA 2. r sin 0 dz dr de

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Q: The figures shown are three similar ARST AUVW ~ AXY Z 2. Find the Values of in Vand tan Y and drag…

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Q: Solve 3 tan(z) = V3 over the interval [0, 27)

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Q: If y = tanh"( k /x) and vx (1 - 9x) y'=A Then A =... Answer:

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Q: Qq / show thot ifa is a constont then, u(X,t) = sin lat) cos (x) is a solution to

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Q: •2/3 Find dx. Hint: try either x = 4 sin 0 or u = 16 – x² as a substitution. 16–x²

A: Topic = Integration

Q: If y = tan x, prove that y``= 2(1+y² )(3+ y²).

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Q: 14. Find a) esin 2xdxb) J vanyt dx, using the substitution x= 2 tane. 15, Find a) fxe"-dx b) dx…

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Q: a2z a2z dz Q3) A: If e-(sinx + cosy), show that ax2 ду? at

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Q: S Si dydx %3D 1-r

A: To evaluate the given double integral.

Q: al equation sin(t) with y( solution for this hen t belongs to ||

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

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Q: V3 Find cosh 0, tanh 0, coth 0. 2 B) If sinh 0 =

A: Given that sinhθ=32 We know that cosh2θ-sinh2θ=1 ⇒ cosh2x=sinh2x+1 cosh2θ=322+1=34+1=74 coshθ=72…

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A: We have evaluate the given complex number z=sinej3+sinh5∠30°

Q: If y= tan x , prove that y`= 2(1+ y² )(3+ y²).

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Q: 6. Evaluate |2 Sin xʻdx, by (i) mid-point rule, and (ii) Simpson's 1/3 rule.

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Q: 1 By writing u y", and using the chain rule, show that 0") = nyn-1. dx

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Q: check by differentiation that y=5COSE 4 Sint is a solution to y"ty=D0 by finding the terms in the…

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Q: 22. Determine Sz sin? y cos y dy

A: Given that: ∫0π2sin2ycos6ydy

Q: - Using Euler's equation, show that- : z fain (K 0)} - z sin Ø z2 – 2zCos Ø +1

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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

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Q: Which of the following is correct? 1. cosh²x + sinh²x = 1. II. sinh x cosh y = sinh (x + y) + sinh…

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Q: 213 If cot 0+ tan = and sece - sece = y, Prove that (x'y)° (xy²)*° = %3D

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Q: Find Duf at P. 3 4 f (x, y) = sin(x – 5y); Р(5, 1); u = i и %3 - - NOTE: Enter the exact answer. Duf

A: This is a directional derivative problem

Q: z) tan(y2 + %3D

A: Given that, wx,y,z=tany2+4zx3x=r2t2y=r2tz=rt2 Then we get,…

Q: I sin(z) cos(z) da : Hint:

A: Given integration is, ∫xsin(x)cos(x)dx We know that, 2sin(x)cos(x)=sin(2x) Now, the integration…

Q: 3) Show that y" +y = 0, given that y = 2 sin x + 3 cosx

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Q: B) Find and It x sin 3z and y= tan 3z dx

A: x=sin23xy=tan 3xWe need to find dydx and d2ydx2.

Q: Use Green's function method to solve the following BVP y" – y = cosx, y(0) = 0, y(ln2) = 2 %3D

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Q: V3 Find cosh 0, tanh 0, coth 0. 2. B) If sinh 0 =

A: Given: sinhθ=32 To find: coshθ, tanhθ, cothθ. Solution: We know that, cosh2θ-sinh2θ=1 Putting…