29. (x² + y²) ds Jc C: r(t) = (1 – sin t)i + (1 – cos t)j, 0 < t < 2n

Q: . If y = tan( sin t (. cos t-1 1 dy %3D show that dt 2

A: The given details are as follows. y=tan-1sin tcos t -1 Observe the chain rule of differentiation as…

Q: -3 Evaluate the triple integral ²³ sin(y²) dz dx dy.

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Q: dw Find the value of- dt at the point (1, In 2 ,0) on the curve x = cos t ,y= sin t, 0 <t< 2n where…

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Q: 5. If the function y = y(x) is such that dy + 2y = x cos r, dr use the integrating-factor method to…

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Q: Solve the IVP y" + y' + 1.25y = 0 with y(0) = 3, y/ (0) = 1 O e-t/2(3cos(t) + sin(t)) O e (3cos(t) +…

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Q: (b) Solve the integral [(3x – y)dx +(2x +3y)dy along the curve x = y' from (0,0) to (1, 1).

A: Solution of question as follows

Q: Obtain the general solution using separation of variables x cos² y dx + tan y dy= 0

A: Given differential equation is: x cos2y dx+tany dy=0 Apply variable separable: tanycos2ydy=-xdx…

Q: 7. (a) Find dy/dx, when x a(1 + cos 0), y = a (e + sin 0). (b) Differentiate xCOsx w. r. t. (cosx)*.

A: Proceed as shown below...

Q: 1- Evaluate: 2y sinx dy dx อน 2- If u = x² + ey², x = sin 2t , y = cost² find Ət

A: Above question is solved.

Q: (. 0) S(x, y) = In(x² + xy), at (4, 1) S(x, y) = sin (x²) + cos y, at

A: 19. f(x, y)=sin(x2)+cos y At π2, 0, fπ2, 0=sinπ22+cos 0                =sinπ4+cos 0…

Q: (4) Evaluate sin(yz)dr+xz cos(yz)dy+ry cos(yz)dz, where C is any curve joining the point (0, 0,0) to…

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Q: dw "(1),y = sin (1),-: 2) w=+ x= cos at =3 Ans. -1 dt

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Q: A particle moves along the x-axis with velocity given by v(t) = 6T sin (2nt) for time t > 0. If the…

A: Given: vt=6πsin2πt at t = 1, x = -4

Q: 8. y = In(2e-t sin t)

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Q: Find dy/dx: y = sin (In x²). A 2 cos (In x²) (B) 2 cos (In x²) / x

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Q: 2,3 Given z = sin (x + y) where x = s²t, y 2s 3t. az as az at

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Q: Given (1 + 3x sin y) dx - x² cos y dy=0 with y(1) = 0. Using Euler method with h=0.1, compute y'…

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Q: (b) Solve the integral [(3x– y)dx+(2x+3y)dy along the curve x = y³ from (0,0) to (1, 1).

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Q: 7. (a) Find dy/dx, when x = a(1 + cos 0), y = a (0 + sin 0). (b) Differentiate xcosx w. r. t.…

A: Differentiation using Logarithms: When a function appears as an exponent of another function we make…

Q: If y = x* cos' x-e* In( 7x +1) , then find dy at x=0. dx 3

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Q: -TL 4.) x² sin(xy) dydx

A: Given ∫0π∫01x2sinxydydx

Q: Let y = tan(4r + 8). Find the differential dy when a = 3 and dæ = 0.1 Find the differential dy when…

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Q: Find where y(x) is defined by d²y dr? (a) 3x2 – e2, (b) sin 3x + cos r, (c) 1+x – x2 + In r. - -

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Q: -7x f(x, y) = e" sin(4x + 5y) af e^(-7x)(4cos(4x+5y))-7sin(4x+5y) af 5e^(-7x)cos(4x+5y) dy ||

A: Partially differentiate with respect to x and y by using product rule.

Q: dz Use an appropriate form of the chain rule to find dt 1 z = 8 cos a – sin xy; x = - y = 4t t'…

A: This question is based on Derivative of Function.

Q: dy 1- Solve = cos x + y, where y = dx 2.0 at x 0 take step size h = Ax=

A: Given,         dydx=cosx+y Where y=2.0  at x=0   and h=0.1

Q: Find the general solution of (cos cos y +ycos x ) dx + (sin sin x – x sin sin y ) dy = 0

A: The given differential equation is incorrect and hence the correct differential equation is as…

Q: dz az B. Find əx and ay 3. x eY+ cos xy36xz+5x²

A: partial derivative

Q: dW Find at t=0, if dt .3, W = x*y+ zxy whe x = sin2t, y = cos ?

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Q: 3. If x = (sin t+cos t), y = (cos t-sin t), (1 < t < 4), evaluate ip, dt. dt dt

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Q: 2. Give an interval of the form (a, b) around r 1 such that the IVP has a unique solution. dy = sin…

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Q: Let y = tan(4r + 4). Find the differential dy when x = 1 and dæ 0.4 Find the differential dy when x…

A: Given that, y=tan4x+4 differentiating both sides with respect to x, we get…

Q: If a = 5+ti and y = 3t - t then dy at t = 1 dz is :

A: as per our guidelines we are supposed to answer only one question. Kindly repost other question as…

Q: What is the characteristic equation for dy 2. dt d²y y +2+e' sin 3t dt 2

A: Characteristic equation for the given differential equation:

Q: Suppose w = In(8x² + 2y² + 3z²) , x = 9 cos(t) , y = 9 sin(t) , and z = 8/t. Compute dw/dt in two…

A: To find: The derivative of w and the value of dwdtt=8  Given: Suppose w=ln8x2+2y2+3z2, x=9cost,…

Q: 25) 2 sin(y)dx+cos(y)dy 0, y(0) = z/2

A: Q 23 is incomplete as it doesnot contain dy term. and Q 25 is in next step.

Q: 3. Find dy/dx of the followings: (а) у | V2 + cos³ t dt 2. •7x2 (Ъ) у V2 + cos³ t dt 2 (c) Y 1 dt t2…

A: using fundamental theorem of calculus part 1 ddx(∫abf(t)dt)=f(b)ddx(b)-f(a)ddx(a)

Q: If x = 2 sin* t and y = 3 cos* t, then find dy at t = %3D dx 4 а. 1.5 b. -2.5 с. -1.5 d. 2.5

A: Solution:

Q: 1. Find fx,fy,andfz f(x,y,z)=sin(xy)cos(yz2)

A: It os partial derivative wrt x y z

Q: find / sin³ x cos³ x dx cos³ 2x sinº 2x dx 11. 12. cos² x dx sin? x dx 13. 14. 16. 7 sin y dy 7 cos'…

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Q: 5. Find dt ,y = cos(sin(t – 4))

A: Given function is: y=cossint-4 Derivation of the above function with respect to t. dydt=ddtcossint-4

Q: 3) I Cos dydx Ins Iny 4) S S e** dxdy X 1 0

A: 3)  Given:      ∫π2π∫0x21xcosyxdydx       =∫π2π∫0x21xcosyxdydx

Q: dz Use an appropriate form of the chain rule to find dt 1 z = 8 cos x – sin xy; x = y = 2t t' Enter…

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Q: If x = 3 sin* t and y = 2 cos" t , then find dy at t = dx 4

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Q: π/3 7. Sp² sin 0 de dp π/6 8. (2-y)dy dx 9. 5/¹¹² x cos y dz dx dy

A: Since you have posted multiple sub parts question in this question which are not interlinked so i…

Q: Show that g(x) = cos 2 =x+3 ™K(x, t) g(t) dt 0 || sin x cos t, 0≤x≤t Y sin texr

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Q: 2²y ds, C:x = cos t, y = sin t, z = t, 0 < t < a/2

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Q: (2e" sin(y) – 4y)dr + (–7x - e cos(3)dy = 0 not exact

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Q: (b) Solve the integral (3x– y)dx+(2x+3y)dy along the curve x = y' from (0,0) to (1, 1).

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