Find the total differential. z = 5x³y4 dz =

Q: Find dy/dx for x?+6xy?+y%= 12

A: Given,          x2+6xy2+y3=12

Q: Calculate the amount of f S'(cosTx)x³ dx. (S' = ds, dx'

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Q: Find 2 dr if y=1-t² and x= 4+² dx

A: 1.       dy/dt = d/dt [ 1- t²]   = -2t        2.      dx/dt  = d/dt [ 4t²]     = 8t   So now…

Q: QUESTION 2 Use differentials to estimate v8.99 + (8.99)² correct to two decimal places.

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Q: dx dy 26.

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Q: Find the most general antiderivative for the function - 4V?. | Antiderivative = ?

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Q: x – 8 dx x² – x – 6

A: Find the integral by substitution method

Q: e 2x dx 4e2 – 8e + 5

A: We have to find anti derivative of given expression.

Q: write a differential formula that estimates the given change in volume or surface area. The change…

A: The volume of a right circular cylinder is,

Q: Evaluate the antiderivatives. 2x dx 5 S

A: ∫2xdx/5 ∫axdx = ax/lna here a =2

Q: Evaluate: [- e2x dx J ex+1

A: SOLUTION-

Q: J dx 4+x²

A: Given,            ∫14+x2dx

Q: I dv= 3x y dx

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Q: S'(1 + v=)dz b)

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Q: J 3X+ 9 e dx

A: We will integrate the following expression using Substitution and integration by parts.

Q: Use differentials to estimate the value of V1.3. Compare the answer to the exact value of V1.3.

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Q: S(8x3 + x-3)dx

A: Solve by integration

Q: Find the total derivative dy/dw. Y=3x+2w+5z? x=4 In(w-) z=ez+3x

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Q: 18 Find J4 dx.

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Q: S. y dk t x dly luhere L=

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Q: yj dy dx

A: Evaluation of the triple integral

Q: dx 2xVIn x (b)

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Q: d?y Calculate dx y = -

A: Derivatives can be defined as rate of change of function with respect to an independent variable. It…

Q: @ yーJ=ex 12 y3=

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Q: dy — ху — 4х dx

A: Given differential  equation dydx=xy-4x

Q: 1+e4x 1+e9x dx.

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Q: xZ dx

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Q: Find dy/dx. x = 3√ t, y = 4 − t

A: Given- x=t3,y=4-t To find- dydx Concept used-  dydx=dydtdxdt

Q: dx J Vx² – 25

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Q: Use differentials to estimate the amount of paint needed (in m3) to apply a coat of paint 0.04 cm…

A: Our Aim is to find the amount of paint required to coat thickness of 0.04 cmby considering a…

Q: Find the differential of the function. p = 7q – 6g3/2 dp =

A: Consider the function, p=7q-6q32

Q: Find 3 J (æ+ 1)/2x² + 4x + 6 dx. OTM

A: We have to find the integral of the given function.

Q: dx + 6х — у = 'y dy

A: Given dxdy+6x=y

Q: Solve for dy when y = <<+3x, x=2 and dx = 0.5. 2.500 0.125 2.625 2.125

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Q: x – dx х — 7

A: Given, ∫xx-7dx    We have to find the antiderivative.

Q: 2 lnt and y: where 1<t<3.

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Q: Find the total differential. z = 8x4 8x4y10 dz = (No Response)

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Q: E(XY)=?

A: Given Data: f(x,y)=17x2y             for (x,y)=(1,1), (1,2), (2,1)           =0…

Q: Find the antiderivative dx/(49x2+16)2

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Q: Calculate dx y = x2

A: ddxxn=n xn-1

Q: 4. Calculate | (6x? + 2ry + 3y?) dx dy.

A: Proceed as shown...

Q: z is jointly proportional to the square of x and the square of y. If z=364 when x=6 and y=5, find z…

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Q: S sec? (3 – 2t)dt

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Q: 6x V3x4 +2 dx

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Q: Given 2x2 - 4x + 6 dx find R4. (round to 4 decimal places.

A: The given integral is ∫122x2-4x+6 dx. Let fx=2x2-4x+6   on  1,2. ∆x=2-14=0.25. Note that…

Q: dy 7. J У Vу2 -бу + 5 y V8 — х2 8. dx

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Q: Determine dx dy if y = r -e' and x In(4f)

A: (1) first we find dydt (2) Second we find dxdt (3) then we find dydx=dydtdxdt

Q: J dx 4 + x² =

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Q: ex V1-e2x 1. S dx

A: