-dx. V1–16z² Consider For the u-substitution u = 1 – 16x², which is the new integrand in terms of u?

Q: dy 4xy+5y2 The DE: can be transformed into a seperable DE %3D dx xy +3x2 in x and z by using the…

A: We have given a differential equation and we have to find substitution to make it variable…

Q: cos (2t + ) dt e21–3 %3D 4 -3 4 64e3 7.

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Q: If the substitution u = x/2 is made, the integral 1-(플)2 dx = %3D -

A: Let's integrate.

Q: Q7 Show that CX,y) =e is Condinuous at co,0)

A: The given function is:  fx,y=e-x2+y2 The given point is 0,0

Q: Let y = V7-T. Find the differential dy when r = 4 and dr 0.2 Find the differential dy when r = 4 and…

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Q: Find the partial integral. + 3y?) dy t.

A: Given that a  integration and we solve this integration by using general formulas of integration. We…

Q: Q2/ by using chain Rule to find dw at t = 1 if dt w = 2ye* – Inz ,x = In(t? + 1), y = tan 1t,z = et

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Q: au a²U dt dx² Show that the local truncation error at the pint (ih,jh) of the Crank-Nikolson…

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Q: Use the differential dy to approximate Ay when x changes from x = 2 to x = 2.04. y = V3x – 2 A. 0.01…

A: Given that: y=3x-2x=2 to x=2.04

Q: The acceleration of a particle moving back and forth on a lineis a = d2s/dt2 = π2 cos pt m/sec2 for…

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Q: Evaluate the integral dx (6х + 5)? y making the appropriate substitution: u = dx (6x + 5)2 II

A: Given query is to find the integral.

Q: dz Suppose that z = x³ – 3y?, x = 4(t³ – 1), and y = Int. Find using the Chain Rule. dt %3D -

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Q: The DE: dY - 4xy +5y² xy + 3x? can be transformed into a seperable DE dx in x and z by using the…

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Q: dy _ 4xy+5y² can be transformed into a seperable DE The DE: dx xy +3x2 in x and z by using the…

A: The solution is given as

Q: 00 1 (b) Calculate the improper integral dx , or show that it (x² + 25)3/2 -00 diverges . Show your…

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Q: a Ex Let mxy+2), x=Git, yosint Find dw at t:3.

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Q: Find he value of ds /dy at u = 2 if s = t2 + 5t and t (u² + 2u)3 du %3D

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Q: QS A) Find IF y = - Ve IF y =-Vt and t sinx

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Q: Compute dy/dx using the chain rule in formula. State your answer in terms of x only.  y = u3>2, u…

A: Given equations - y = u3+2           .....(1)                                                  In…

Q: 4. Determine the c, and c2 so that the y(x) = c,e-* + cze8x + sinx that will satisfy the initial…

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Q: dw Use the Chain Rule to find dt w = x²e²y cos(32), x = cos t, y = In (t + 2), z = t

A: The chain rule states that the derivative of f(g(x)) is f'(g(x))⋅g'(x).

Q: Evaluate the double integral : 9. dy dx 0, 22

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Q: Given: y = sqrt(u)  ,  u = 2x2 + 3x + 4 Determine dy/dx at x = -3 a) Using Leibniz Chain Rule b) By…

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Q: Find the Complete or Particular solution OF the Followoilng diffi rential equations: (2メコ+ )dx -2メよ…

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Q: -2-x Q1) Evaluate the integral S* dy dx using polar coordinate 0,

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Q: Let y = 5,a. %3D Find the change in y, Ay when r = 5 and Ar = 0.2 Find the differential dy when r =…

A: Our problem is let y=5√x First, it is easiest to take the derivative of this when in a different…

Q: Q5. Evaluate the triple integral ²³ cos (y²) dz dx dy.

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

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Q: Let y = tan(3r + 4). Find the differential dy when z = 2 and dr 0.1 %3D Find the differential dy…

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Q: Q₂) Compute Z² dz along the straight line from (0) to (4 + 4i), then verify your result by using…

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Q: Let z(x, y) 2x2 – 3y? where a 2s – 4t & y = 9s + 8t. he at dy dx az Calculate ds dz by first finding…

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Q: Find the orthogonal trajectories of r^n= a^n cos . given that r(1) = 13

A: Hey there since you haven't mentioned any angle of cos therefore i am assuming it to be cos (n…

Q: Evaluate the integral. V16-a? 1 dy dx dz = -V16-x2 (x2 + y?)1/2 -4.

A: We can solve as follows

Q: O from the equation z = In(x² + y²) + Zyy Show that zxx %3D

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Q: 2. Solve the IVP 2x + y + 2xyy' = 0, with y(1) = –2. d (Hint: This ODE is neither first order…

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Q: @ Consider the DE, dx %3D dt x (2t -7) What meho can be uoed

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

Q: 2. Give an interval of the form (a, b) around r 1 such that the IVP has a unique solution. dy = sin…

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Q: dz Use the Chain Rule to find : z = = cos(x + 4y),x = 5t*, y = - %3D dt

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Q: Find the total differential. w = e3Y cos(5x) + z5 dw

A: The total differential of a function w= f(x,y,z) with continuous first partial derivatives in a…

Q: dw Find using the appropriate Chain Rule for w = cos(4x−4y), where x = tº and y = 3. dt

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Q: Consider the DE d²y dy dx? 6y = 12x, y(0) = 1 dx 1 is a solution of the DE and determine 3 Verify…

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Q: I = 1- 6x?y dx dy.

A: In double integration, we start integrating from the inner part with respect to the inner variable.…

Q: Use the differential dy to approximate Ay whenx changes from x = -2 to x = -1.96. %3D y = x² + 1

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Q: a. Apply the Runge-Kutta method of 4th order to find the approximate value of y for x =0.2, dy in…

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Q: (dy/dx -y =sin3x) is * O Homogeneous Non Homogeneous O Non of the above

A: The given differential equation is                                                dydx-y=sin3x…

Q: ds Find where Vt +s = 2s . %3D dt

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Q: Q2) Use the chain Rule to find dw\dt of y w = =+2,x = cos²(t), y = sin² (t), z =, at t = 3

A: In this question,w is function of x,y,z and x,y,z are the function of t so first we find out…

Q: Find where) i ) et u*rany tany = 1 , U= xInx (use chatn reule ) ii) coscxy) - * + e+y) = 2 yz

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Q: Determine the solution of y dt + (2yt + I) dy -Ogiven that given that y (-1) = Q

A: 2. We need to determine the solution of the differential…

Q: Let y = -. Find dy and Ay at x = 9 with dx = Ax = - 1. Enter the exact answers. dy = Ay =

A: Solve by using differentiation