dw Evaluate -at the given value of t : dt w =z - sinxy X =t y = Int %3D

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Q: Find the area of the surface that is obtained by rotating the curve Y = 0.25X? – 0.5 Log.X, 1<X< 2…

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Q: Find dw/ dt at the given value for the following functions 1) w=x + y, x= cos(r). y = sin(?), at 1 =…

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Q: dz evaluated at dt If z=tan In with x=sec t and y=eª. Then the value of t= 0 is equal to ...…

A: Chain Rule Let us consider the function z=f(x,y) where, x=g(t) and y=h(t) Differentiate the function…

Q: Determine the total differential, dz. f(x, y) xye® 5xy Factor each part completely. dz =

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Q: Find dw/dt at the given value for the following functions dw Ans. dt 1) w=x+y, x=cos(t), y sin(t),…

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Q: Int Consider R(t) = (t lnt, 1 (tInt, | Ř(t) dt. Find 2 t t(1 – In² t).

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Q: Find dw/ dt at the given value for the following functions dw dt 1) w= x + y°, x= cos(t), y= sin(t),…

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Q: Evaluate the following by changing the order of integration: dx dy. z/3

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Q: Assume X and y are functions of t. Evaluate DY/DT for the following. y^3=2x^4+6; dx/dt=2, x=1,y=2…

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Q: The area under the curve parametrized by x(t) = e", y(t) = 2et +1, where 0 St<1/3, is equal to.

A: As given, x(t) = e3t  y(t) = 2e3t + 1 where 0≤t≤13.

Q: Find the total differential. w = = x?yz° + sin(yz) dw =

A: In partial derivatives, the total derivative approximates the function with respect to all of its…

Q: da dy 3x? – 1 and dt Find at z = 1 if y = at x = -5. dt da dt

A: topic - derivative of a function

Q: t +t dt

A: Antiderivative: Integration is the inverse process of differentiation.  The operation of finding the…

Q: Vi (1 + t) dt

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Q: The surface area of a sphere is expanding at the rate of 6 cm²/sec, Wher What is the change in the…

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Q: If V is the volume of a cube with edge length and thecube expands as time passes, find dV/dt in…

A: The edge length of the cube= x So the volume= V= x3

Q: Evaluate by changing the order of integration: IL sin y³ dy dx 0.

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Q: dy sin?x -- 2у сot х %D dx cot x is The integrating factor of the linear DE of order one

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Q: Use numerical integration to evaluate the following: dx (b) e-" sin y dy 2 x(x + 2)

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Q: dw at the given value of t: dt Evaluate w =x2+y x = cost +sint y = cost -sint %3D 2.

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Q: The volume of a sphere is expanding wherer = 2t. What is the rate of change in volume with respect…

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Q: Find the indefinite integral a. + +k] dt S [Int i а. b. S sec? ti+ dt 1 1+t2

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Q: Find the differential of each function. (a) y = etan(at) (re" tan(xt) gec²nt) dt Pa1)di dy = sec“nt)…

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Q: Find the integral. (Use C for the constant of integration.) (t + 3)cos t2 + 6t) dt

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Q: Evaluat the integral, dx dy y's зу

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Q: Find the approximate value for f(z, y) = sin(x5zy+ ln(y)) at (0.03, 1.04). Taken = 3. 00,24 O 0,14 0…

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Q: The integrating factor of the linear DE dy + ycot x = sin x dr

A: Given: dydx+ycotx=sinx

Q: Find the total differential dw. 4. w = e*" – sin(yz) -

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Q: Find the general indefinite integral. (Use C for the constant of integration.) sec(t)(4 sec(t) + 3…

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Q: th² (t) В V = 2

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Q: Evaluate 2xz dV where E = {(x, y, z) | 2 < x < 4, x <y < 2x, 0 < z < x + 3y} . E Round your answer…

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Q: determine an integrating factor for the given DE? (−xy sinx + 2y cosx) dx + 2xcosx dy = 0

A: we have to find the Integrating factor of the given differential equation

Q: Find the total differential. z = x sin xy

A: Given: z=x sinxy To determine: The total differential of the given function.

Q: The radius r and height h of a right circular cylinder arerelated to the cylinder’s volume V by the…

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Q: Evaluate the integral. (Use C for the constant of integration.) t5 In(t) dt

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Q: Reverse the order of integration and then evaluate. a. Sx? sin(xy)dxdy а. 'y

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Q: a. Sx² e3*dx b. St sin t dt

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Q: dw at t = 4 for the function w(x, y) = e y - In x; x = t 2, y = Int. Evaluate dt O 1 2

A: Given that       w(x,y) = ey - ln x         x = t2 ,  y = ln t

Q: b. Find by double integration the area enclosed by the curve r= a(1+ cos 0) between 0 = 0 and 0=T.…

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Q: Find the total differential of z = In(x + y), x = w, y= w?. By how much will z change if w increases…

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Q: Evaluate the double integral: ¹ sin(x³) Lo Sc vy vy (Hint: Change the order of integration to dy…

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Q: The volume V of a right circular cylinder of radius r and height h is V = Tr²h. (a) How is dY…

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Q: Find z = f (x, y) and use the total differential to approximate the quantity. (2.01)2(9.02) − 22 ∙ 9

A: The given quantity is 2.0129.02-22·9. It is of the form of fx+∆x,y+∆y-fx,y. Here, x=2,y=9 and…