.If z = e-(sin x + cos y), show that a²z a2z az ax2 ду? at

Q: ду Let y = In Vx² + 2z3 + cos(b³), find

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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: Show that 0, if m if m + n sin(nx) sin(mx) dx T, = n IT

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Q: -3+ Sin zt dt 7 8-1 i uct-1) } e-zt 9- to

A: As per our guidelines I am solving only 1st for others kindly resubmit the question mentioning that…

Q: 3. Find dy, where; a) cos(ry) - e 2 elx+y). b) ė?+ Ptany =4, u= xlax (use chain rule)

A: We have to find the derivative

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: az (b) Determine the by using the Chain rule with the following information: ds z = cos (x"y) – sin…

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Q: Suppose tan u = %¾ (sm u>0) and tanuo12/5 Ccasx cO]. Ead he exsee velos OR the followly trgeronetnc…

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Q: Compute / 7(t)dt for 7(t) = (t – 2t, 7, cos (2t)) %3D А. 1 sin В. B. G*-t, 7, sin (2t) ) + č С. tA –…

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Q: Evaluate cos zV1+ cos². dædy

A: Given double integral is                    T=∫01∫arcsinyπ2 cosx1+cos2x dxdy ⋯⋯⋯⋯⋯⋯ (1)

Q: If I, = e cos" zdr, where n > 2, Prove that i) I, =1-n e sin z cos"- rdr

A: Given,  In=∫0π2e-xcosnxdx solving by using Integration by parts, Formula of integration by parts,…

Q: If xty= 2e Cos Øand x-y=2ies.m Ø show that Su

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Q: -W : By the same way, prove that g Z sinWo sinw.k Z -27 cus Wo +1

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Q: Q6:-Prove that: y" = 1 if y=;csc (tan"

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Q: 1 dy sin¬' x If y = xv1 – x² + sin=1 x, prove that 24 – 2

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Q: 5. If y= tan x, prove that y``=2(1+ y² )(3+ y²).

A: Prove the given equation

Q: (b) If u = x? cos y+ye», where x= s+2t and y = st, prove that ди 2- ди = (s – 21) (x² sin y – xye" –…

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Q: 9. Let r = 3 sin tî + 3 cos tj + 4tk. Calculate N

A: Given r(t) To find N(t)------ unit tangent vector

Q: Find / sin(2r) PV -dr R I +4 by invoking Jordan's lemma.

A: Sol

Q: If ſ cos* xdx = Ax+B sin 2x+C sin 4x +D, then {4,B,C} equals S3 1 1] 18 32 4 [3 1 1 (b) 8 4 32 ƒ1 1…

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Q: Show that - if W= cos (メ+y)+ Sin(メ-y) Wメメ Wyy ニ

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Q: 6. If w=xy + yz + zx. x =r cos0, y = r sin0, z= r0, Find dw/dr, dw/dO, when r = 2,0 =x / 2.

A: Answer

Q: If f(x,y,z)=In(x²y+sin² 12

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Q: H.W: if w x2 + y2 + z2, x= e*Cos6, y-erSin0, z=e0 prove that aw/ar= er/w and aw/a0 = e20/w

A: I am going to solve the given problem by using some simple calculus to get the required result of…

Q: Suppose that w = a7 · exp(2y) · cos(4z) with z- in (+ 5), x = sin (t+ y = In (t +2), z = t.

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Q: azz = e2x-y + cos(-3x + 2y) + 3x, дхду Given that az where əx 5x2 – sin (3x) when y = 0, and Z =…

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Q: Find if z = sin(uv)cos(uv), where u = e' and y = e2t. dt %D Lütfen birini seçin: O A. 3e(sin2(e3t) -…

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

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Q: 3. If y = w sin w, then what is dy/dw??

A: y=wsinwTo find d2ydw2

Q: dq + q = 4 cos 2t dt

A: Given that, dqdt+q=4cos2t On comparing with general equation dydx+Py=Q ⇒P=1, Q=4cos2t, dx=dt…

Q: 2-If w(x, t) = Sin(x - + 3t) + Cos(2x+ 6t), prove that wtt = 9wxx %3D %3D

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Q: For the IVP: (1-4) cos ty"-In(r-1)y+VT+5y=e, y(2) =1, y(2) = 1

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Q: dø +3ø = sin ot on (0,+∞) dt [$(0) = 1.

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Q: (b) If u =x cosy+ ye», where x=s+2 and y= st, prove that 2- ds du - (s - 21) (* siny-xye -e").

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Q: /Prove that the value of cos()dz, when z = T + 2i is e + e-1

A: Complex integration of the function

Q: Find ſ z2 sin z dz

A: We can find the integral in the following steps

Q: If u =x² cos y +ye», where x =s+2t and y= st, prove that ди 2- Əs ди 3 (s— 21) (х' siny — хуе" —…

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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: - Show that u(x,t) e-a't[A sin(2x) + B cos(Ax)] satisfies the PDE uz = a?uxx for arbitrary A, B and…

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Q: D. If z = In(x – y) + tan(x + y), show that Z = Z y XX

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Q: (b) If u = x² cos y+ye", where x = s+2t and y = st, prove that ди ди 2 = (s – 2t) (x siny– xye –…

A: u=x2cosy+yexyx=s+2ty=st

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

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

Q: Show that J, (z cos0)d0 = - R/2 os e)de = 1-cos z %3D 21

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Q: -1 If cos x+cos y+cos z= T, prove that x +y +z +2xyz = 1

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Q: Show that w°sin(xw) пе dw= 2 cosx if x > 0. w* + 4

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Q: In AXY Z, the mZY = 90°.XY = 19 and XZ = 22. What is cos X? ООО О

A: Given,

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: (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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