f (t) = 3e" cosh (In 2r -2t

Q: dy In(3x + 7) Find for y = dæ 9e5z dy %3D dx

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Q: Without finding a potential function, determine if G : , 2y^x is conservative.

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Q: Find dY at x = -1ifY zu%5V=4 3. and u= X²+ X

A: Given that y=u3+5u-4 and u=x2+x We need to find dydx at x=-1 Take y=u3+5u-4 Substitute "u"…

Q: t2 + 4t + 10 -dt t3 + 2t² + 5t dy J 3 + 5cosy

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Q: dy Find at t = a where dt 1 7. у %3D = 3s + 2 and s t2 when a =1. + 4

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Q: ven f(x,y) = -2xy² where x = 5t and y = 8t2. Findf' (t) at t = 3. %3D

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Q: Can you help me step by step?

A: Differentiate both sides w.r.t. t. Apply product rule on the right side. Product rule: (uv)'=u'v+uv'

Q: --——-^*[e'-In(2t+1)]dt, find g'(x) . dx 4 A e*+ (2x + 1)² 4 B et + (2x + 1)² 2 (C) e*- - (2x + 1)²…

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Q: Q4/ 1- Evaluate: f/2fy sinx dy dx ди 2- If u = x² + ey² ,x= sin 2t , y = cost² find at

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Q: The area between the curve X= t2 - 2t+1, y= In(t) and the y-axis for 1sts5 would be found by setting…

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Q: Evaluate the integral 2 dx where fx) if -2 s xs 0 16-2 if 0xs3

A: Given function is The integral isThe integral can be written as: Plugging the function and applying…

Q: Solve using product rule d(uv) = u dv + v du: f(x) = (3x^2 – x + 4) (2x^2 – 1)

A: Our Aim is to solve the given function using the Product Rule where f(x)=(3x2-x+4)(2x2-1)

Q: Find the total differential. w = (3x + 4y)/(y + 3z)

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Q: Q4) Find y" + 3y' 5y at x=5 where y = xsin(1/cscx))

A: Solution:-

Q: Express the general solution of dy/dx = 1+ 2xy in terms of the error function erf(4) = dt.

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Q: Solve the ODE: dy (x' +4x) 0 using separable variable method: dx x(sin 2y +4)

A: The differential equation is as follows : dydx-(x5+4x)x(sin2y+4) = 0 Hence we get dydx =…

Q: 2 4 Q3) Evaluate the integral || xe" dy dx 0 x?

A: LetI=∫02∫x24xey2dydxchange the orderI=∫04∫0yxey2dxdyLet∫0yxey2dx=x∫0yey2dx∫0yxey2dx=ey2[x22]0y…

Q: Integral of (dt)/(t^2sqrt(t^2-16))

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Q: dy t² +3 21. Find 9 if y = In dt /1-t,

A: We need to find derivative of given function with respect to t

Q: Find the total differential. z = 2x6y9 dz

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Q: Q4) Use the chain rule to express dy /dx in terms of x and y t2 y = t2+1 and t = 3x3 – 3 where x =1

A: Given y=t2t2+1 and t=3x3-3 and x=1

Q: [-+] 5t dy 3.1는-51%3D-y dt

A: This is a linear 1st order differential equation.

Q: Find the total differential z = 1/2 (ex2+y2− e−x2−y2)

A: The given function is z=12ex2+y2-e-x2-y2. Note that  ∂z∂x=12ex2+y22x-e-x2-y2-2x=xex2+y2-e-x2-y2…

Q: d csinx 1 dt 1-t2 dx '3 V5 SNt VE2 + 1 dt 1+xv

A: We have to solve the integral

Q: Y 30 ΨΥ Ỉ2 2 47 13 23 24 με χ ΕΙΝΑΙ Fino η Exy. ἐκ ἔγ In ex² - (Ex)^ in [y- (fy) th nexy- έχτι…

A: Given information: X Y X^2 Y^2 XY 27 30 729 900 810 44 19 1936 361 836 32 24 1024 576 768…

Q: Find dy/dr by differentiating implicitly if z +ry- 6r = 2.

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Q: Find the total differential z = 5x3y2

A: The given function is z=5x3y2. Total differential: Let z=f(x,y) be continuous on an open set S. Let…

Q: sin(2t + ) dt e21-3 4 7 4 4 64e 7

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Q: d²s ds + dt 4t + 2cost where s = 0, ds/dt = 0, t= 0 dt2

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Q: Find the total differential. z = 5x3y8 dz =

A: The solution is:

Q: Find the total differential. z = 6x1°y8 dz =

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Q: Find dy/dt. 13) y - cos (πt - 19) 14) y = 4t(5t + 2)4

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Q: Integrate f(x) = 0.5 + 20x + 3x4 from a=0 to b=3, given N=12 by using a) Simpson's 3/8 approximation

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Q: Q3) Compute for y(x) = csc3(4x) + 2x – 3 and x(t) = 4sin t² at t=1 dt %3D

A: Let y(x)=csc3(4x)+2x-3 and x(t)=4sint2 Differentiate y(x) with respect to x…

Q: Find the total differential. z = 10x4y5 dz = (No Response)

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Q: 3 In (sec v) 2t Evaluate the integral ex dx dt dv. 00

A: Topic = Integration

Q: 51. grad f = (2x + 3e")7 +3xe'j

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Q: 2s Prove that L(t sin t) (s²+1)²

A: We can use the concept of Laplace transform in order to solve the given problem.

Q: d²x dx + 4 + 5x – 10 = 0, when t dt 0, x = 0, x = 0 %3| %| dt2

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Q: -2t f(t) = te "sint s + 2 2s + 4 (s + 4s + 5)- s´ + 2S + 1 3 j O خيار 1 S 2s + 4 (s² + 4s + 5) S¯ +…

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Q: Find the total differential of z = In (2x – 3y).

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Q: Q4) Find y" + 3y' 5y at x-5 where y = xsin(1/cscx))

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Q: #@3 g (x; y) = 7x3 - 49IXY + 7y3 Find and elassify all the extreema of the fine tion

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Q: 3. Integrate! 12e-0.21 а) -dt b) 6r 3,2 Se041 dr dx c) f- x. V1+ In 3x?

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Q: 2t + 1 What is the indefinite integral of dt t3 -8t + 21t – 18

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Q: L{sin(JF)} = V %3D 4s 2.s2

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Q: Find the differential dy. y =  x + 8 7x − 1

A: Assuming that y is given as:

Q: Q2: Evaluate the integral S Vx² – 2x + 1 · dx 3,

A: To Evaluate: