37. F(x, y, z) = xi + yj + zk C: r(t) = 2 cos ti + 2 sin tj + tk, 0 < t < 2n

Q: Find the total differential. w = x7yz9 + sin(yz) dw = 7x°yz° dx + 6.9 7_9 +2 cos (yz) )dy + (9x'yz°…

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Q: Compute for the general antiderivatives of the functions 1. [2 sin x cos x dx 2. ſe2x dx

A: Given integrals, 1. ∫2sinx cosx dx2.∫e2xdx

Q: 1 If f(x,y) = tan-(x y) with x= cos(2 t),y= then sin(2 t) " df can be calculate as follwos: dt O1.…

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Q: dz Use an appropriate form of the chain rule to find dt z = 7 cos x – sin xy; 1 y = 3t t' Enter the…

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

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Q: (t + z cos(t)) dt + (sin(t) – 3z² + 5) dz = 0

A: Let's find.

Q: f) y= xcos(xln x) g) y= 3(sin 2x – x* }** In. 3x'e** h) y= cosx

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Q: Let w = x2e2y cos 3z. Find the value of dw/ dt at the point (1, ln 2, 0) on the curve x = cos t, y =…

A: Given: w=x2e2ycos3z x=cost y=lnt+2 Putting x, y and z in w, we get…

Q: 27. w = xy + yz+ zx, x = r cos 0, y = r sin 0, % = r0; %3D dw dw when r = 2,0 = T/2 Ər' d0

A: Given that,  w=xy+yz+zx , x=rcosθ, y=rsinθ and z=rθ. To determine the value of ∂w∂r, when, r=2 and…

Q: .3 Suppose that w = x³yz + xy + z + 3 and x = 3 cos t ,y = 3 sin t , dw z = 2t. Evaluate dt t= ドIN

A: Ans:  we will use product rule of differentiation to solve this question.

Q: Let w = x^2e^2y cos 3z. Find the value of dw/ dt at the point (1, ln 2, 0) on the curve x = cos t, y…

A: Given  By chain rule of differentiation , we have

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: dz is equal to .. dt Let z= In (x2+y²) where x=ue"sin t and y = ue"cos t. If u= -2 and t=0 then -

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Q: Find a homogeneous (linear) DE with a following FSS: y1(x) := 1; y2(x) := sin(5x); y3(x) := cos(5x)

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Q: SO FO %A4 Find dy/dt. y cos(W10t +1 -sin(ot +11 5. sin(~10t + 11) II + 301 +101 sin(~10t + 11) II +…

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Q: (x,() + x(x, t) = sin(t) u(n, 0) = cos(7), at %3D %3D nER.

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

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Q: Find dy/dt, x=4 sin t; y=12 cos t* O 24 cos t O -24 sin t O 12cos t O -12sin t

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Q: dz at t = dt if z = f(x, y) = x² – 3xy+ 2y², x = x(t) = 3 sin 2t, y = y(t) = 4 cos 2t. Use chain…

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Q: dz Use an appropriate form of the chain rule to find dt 1 z = 4 cos x – sin xy; x y = 7t t' Enter…

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Q: Compute cos(x) cos(y) dx – sin(x) sin(y) dy, where c(t) = (9t, 4t2), o sts 1. (Round your answer to…

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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: 22. u- Vr? + s, r- y + x cos 1, s -x+ y sin t; ди ди ди when x= 1, y = 2, 1 = 0 ar ay at

A: Given: u=r2+s2  r=y+x cos t and  s=x+y sin t By using Chain Rule we have to find: ∂u∂x, ∂u∂y ,and…

Q: Solve the DE sinx siny dx + cosx cosy dy = 0 by separation of variables. cos y A sin x B sinx cosy =…

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Q: find dy/dt Y= (1+cos4t)^5

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Q: Solve the DE Ssinx siny dx + cosx cosy dy = 0 by separation of variables. sin y A cos X B sinx cosy…

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Q: 6. Let z = 5e** sin y . Compute the differential dz. A) dz = 20et* sin y dx + 20e** cos y dy B) dz =…

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Q: 2 1 Evaluate the iterated integral42x°y® dy dx. 56 -1 0 2 1 | 12*y®dy dx= [ -1 0

A: Consider the integral

Q: 22. u = Vr² + s², r = y + x cos t, s=x + y sin t; ди ди ди əx’dy when x = 1, y = 2, t = 0 dt

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Q: 21 Find Ez hox) Cx siny +y cosy)it hex cxcosy-ysiny) 5 aanon Ze o Pn hex) for which conserrabive on…

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Q: Find the differential dy: y = sin(x√³). Ody = COS cos (T√²³) [2√T™- 2 O 0 O (E) None of these…

A: A detailed solution is given below.

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: 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: 8) Let z = y-x². Use differentials to estimate dz when x = 1,y = 5, dx = 0.03, and dy 0.1. !! %3D

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Q: dz Use an appropriate form of the chain rule to find dt 1 z = 6 cos x – sin xy; Y = 8t %3D t' Enter…

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Q: dw 3) Find ifw = 5 cos(xy) – sin(xy),x = ,y = t,z = t³ - %3D dt

A: Given: w=5cosxy-sinxy, x=1t, y=t, z=t3 For finding dwdt, first we find w in terms of t So, we put…

Q: Find dy/dt. 7) y= (ecos(u7)4 A) - esin(u7)3 B) co4 cos(/7) COS e3 cos(t/7) D) - sin e4 cos(t/7) Find…

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Q: 4. Find дw b. dz a. дх at the point (x, y, z) = (0, 1, T) if w = x² + y? + z? and y sin z + z sin x…

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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: Solve the DE sinx siny dx + cosx cosy dy O by separation of variables. cs y = C sin x A В sinx cosy…

A: Solution

Q: dz Use an appropriate form of the chain rule to find dt 1 z = 5 cos x – sin xy; y = 4t t' X = Enter…

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Q: does not exist. (b) If u = x cos y+ye", where x=s+2r and y = st , prove that ди ди dt = (s – 21) (x²…

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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: By (d) dy 2- = 3t + 2, y(0) = y'(0) = 0. dt By +4 dy + 20y = -3 sin 2t, y(0) = y'(0) = 0. (e) dr² dt…

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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: Find, if y (3 z)t* + cosec (t) + Z In(2t + 3) dt2

A: First of all, let's get rid of Z by substituting Z = 43 in the equation above: y = (3 x 43)t4 +…

Q: Find the differential dy of the function y=(cos(x))(7x) a. dy=-7x(sin(7x))dx b. dy=(-cos(x))(7x)dx…

A: To Find the differential dy of the function y=(cos(x))(7x)

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

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Q: Q: If In/x2 +y2 =sec(), use implicit differential to proof the following: - dy (²+y*). sec?. tan?…

A: lnx2+y2=secyx

Q: dy dt 1 Find dx if 2y°t + t°y = 4 and d.x Cos t

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