find ow/ar if w = (x + y + z)², ar www w x = r – s, y = cos(r + s), z = sin(r + s) at the point (r, s)=(1, -1)

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A: Given : F(x, y, z)=(x²  + 3y ,  y² -4z ,  sin(x )cos(y) - z2 )  Now we find div F = ?

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Q: Find the Differential of a Composite Function Original function                        y = f(x) =…

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Q: test for the exactness of the differentral dy + Cosx +Sinyfy -0 quation And hence find the Salution…

A: A differential equation contains independent variables, dependent variables, and the differential…

Q: Determine the integrating factor of the Bernoulli's equation given pelow: dy -y cot2x = y' csc2x dx…

A: ................(1) substitute take derivative .................put it back in equation 1

Q: Solve for dy given xsin y - ycos x = 2 | dx sin y-ysin x А. cOS X-XCOs y sin y+ysin x В. coS X-XCOs…

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Q: sen z + cos x dz | (tag z + 1) dx = In sec x+z + C 37. %3D cos 2

A: 37.   Given integral, ∫sen x+ cos xcos xdx

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Q: Find the Integrating factor of: dy + y. sec5x = tan5x dx 1 (sec5x + tan5x) 5 O sec5х — tanп5x + 5 O…

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Q: Two functions u and r of x and y are said to satisfy the Cauchy- Riemann equations if u, = v, and u,…

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Q: show that the differential forms in the integrals are exact. Then evaluate the integrals.

A: Given: ∫(1,0,0)(0,1,1)sinycosxdx + cosysinxdy+dz To Show: (a). Differential forms in the integral…

Q: Write down an integral expressing the length of the curve y = cos x, 2 2

A: Apply the below formula: L=∫ab1+dydx2dx

Q: (ysin x+xy cos x)dx+(xsin x+1)dy = 0 Ans. xy sin x+ y = c

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Q: Find F'(x), where F(x)= int. of ((t^2)+1)dt, from sin(3x) to x=-4. Use the 1st rule of the…

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Q: 」enr一2) dz csc (4r – z) dz dz dz 17. 2 V1 – sen 2z V1 – cos (4- – 2z) In | csc (4- – z) – cot (†7 –…

A: Integrate as general

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Q: Pind the ualue of e is an integrating facko of ly-y')+xy'so

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Q: In evaluating, 2x cos (2x) dx using integration by parts, identify the portion of the integrand to…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: express the length of the curve as an integral but do not evaluate it. r = (2 − cos θ )−1, 0 ≤ θ ≤…

A: Definition used -                Length of the curve -            L=∫αβrθ2+r'(θ)2dθ

Q: Compute TOT/ cos(y³) dydx. [Hint: Change the order of the integration.] Show your solution. Select…

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Q: Ssin x x cos x dx = %3D Select one: а. -cos 2x +C 4 b. -cos x + C 4 c. -sin 2x + C 4 d. -sin x + C 4

A: We need to evaluate the following integral ∫sinxcosxdx

Q: Let x,(t)-v(t)+sin(r), x,-vt) then x,(t)= xN-cosit) Select ones True, False

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Q: aーメ ターメ2.y to い-X to cylindHcal coordin ates

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Q: d sec z = sec z tan z dz

A: The function is a rule that associates or fixes a number to the particular point z . If , then the…

Q: dt dx2 dy , ди u(0, у, 1) dx (1, y, t) = 0, и(х, 0, г) %3D ди - (х, 1, г) %3D 0, dx и(х, у, 0) %3D 2…

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Q: sin(t) et, X2 sin(t)- cos (t) and X3 D sin(t) + cos (t)] 0. Given that X, cos(t) sin(t) + cos (t)|…

A: The problem is wrong, three vectors are not linearly independent.

Q: Dete‎rmine if f (x, y) = ={(xsi‎n3y)/(x‎2+y6), (x, ‎y) ≠ (0, ‎0) ={1, (x, y) = (0, 0) is‎…

A: Solution: A graph for a function that's smooth without any holes, jumps, or asymptotes is called…

Q: cotu. vX + vy + y %3D If u = show that x ax ay = CoS coS х - у

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Q: Determine if F=(e* cos y + yz)i + (xz-e* siny) j+(xy+z)k is conservative. If it is conservative,…

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Q: Integral of cos2x on [0, infinity]

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Q: ) Compute f-(, ") and fy(§, T) of f(r, y) = e9 cos(ry)

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

Q: Show that z - sinh z Res i | 2 z sinh z z=ri

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Q: Solve using determining the integrating factor: cos x dx + (1 + 2/y) sin x dy = 0. %3D

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Q: find div and curl F F(x,y,z)= 7y3z2i- 8x2z5j-3xy4k F(x,y,z) = exyi-cosy j +sin2 z k

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Q: Find a potential function for F(x, y, z) = (y² cos z, 2xy cos z, –ry² sin z). %3D COS

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Q: Apply integration by parts: S udv - S vdu = uV sin2x – cos2x dx sin2x + cos2x

A: Given function is sin 2x-cos 2xsin 2x+cos 2x. Integrate using integration by parts. Chain rule of…

Q: Evaluate fsin( sin (Inx) dx Integration by parts will be used repeatedly. What is the expression…

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Q: (a) If f(x.y) = e siny - e sinx then verify that fry fyz- %3D

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Q: show that the differential forms in the integrals are exact. Then evaluate the integrals.

A: Here, we have   Assume ∫(0,0,0)(2,3,-6)2xdx+2ydy+2zdz                   (i)   Using the formula,…

Q: Find fyxyx for f(x, y) = ln(xy) − cos (xy) at (1, π)

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Q: 1. (sin y — y sin x)dx + (сos x + х сos y — у)dy 3 0 %3D 2. (1— 2x2 — 2х) у' %3 4x3 + 4ху 3. (Зx cos…

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Q: 3. A particle is located at a distance x meters from the origin, a force of x +2 newtoms is acting…

A: To find the work done

Q: 3. S sin(3x) cos(5x) dx

A: To evaluate: I=∫sin (3x) cos (5x) dx

Q: isolated singular point 1. z/((z^3)+z) 2. exp(tan(1/z)) 3. (1/(z^2)) * exp(1/(z^2)) z=4 is apole of…

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Q: Find the integrating factor μ(x) of y' + 4y - tan(x) = 0 such that μ(0) = 1. μ(x) =

A: See the details solution in below

Q: dy +Hanx Siny = I Cos y die

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Q: 5. Use integration to find the exact area outside r = 4 cos 0 and r = 4 sin 0 but inside r = 2.

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Q: Change the order of integration 2 rIn(r)+1 f(r,y) dy dx Ji Ji

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