Find f. (Use C for the constant of the first antiderivative, D for the constant of the second antiderivative and E for the constant of the third antiderivative.) f'(t) = Vt - 2 cos(t) f(t) =

Q: a) Find the differential dy, and b) evaluate dy for the given values of x and dx. y = e*/10 x = 0,…

A:

Q: Find the value of dz and dz/ dy at the point A when x changes by (0.01) and y changes by (- 0.01) xe…

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Q: For functionf (x, y) = e*y + cos(x – y), write the first and second order full differentials

A:

Q: Find the differential dy of the given function. (Use "dx" for dx.) y = 4/x + dy

A: find dy

Q: Let y 5x? + 5x + 2. || Find the differential dy when x = 5 and dx = 0.3 Find the differential dy…

A: GIVEN: y = 5x2 + 5x + 2

Q: Let y = 2x². Find the change in y, Ay when I = 4 and Ar 0.1 Sesse Find the differential dy when = 4…

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Q: Let y 4 Find the change in y, Ay when ax = 0.2 4 and Ar Find the differential dy when 4 and da 0.2 =

A: Change in y is,

Q: Find the differential dy of the given function.

A:

Q: Find the differential dy of the given function. (Use "dx" for dx.) y = xV9 - x² = Ap

A:

Q: t +t dt

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

Q: dy=(0.5x- 3) Co 3)° dx

A:

Q: Let y=e^(x/2).Find the differential dy when x=1 and dx=0.3 Find the differential dy when x=1 and…

A: Given function is The differential dy is evaluated as follows,

Q: Let y = 4/T. Find the change in y, Ay when a 3 and Ar Find the differential dy when x 3 and dx 0.2

A: fx=4x here x=3 f3=43 . Δx=0.2 fx+Δx=4x+Δx f3+0.2=43+0.2 f3.2=43.2 . Δy=f3.2-f3 Δy=43.2-43…

Q: f(x) = 9x3 + 4x.   Find the differential of the function.   dy =?

A: Given , y=fx where fx=9x3+4xwe have to find the differential dy

Q: Find the differential of a) y=s/5+3s b) y = e−u cos(u)

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Q: Find the total differential. w = e²y cos(7x) + z³ dw = (No Response)

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Q: If z = cos x - e¹, x = 1² + 1 and y = 5 + ln t, then equals: dz dt

A:

Q: Find the differential of the function. z = e ** cos(8nt)

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Q: Find the antiderivative of the given derivative. ds = 5t(212 – 1)3 dt

A: Solution:-  given that  dsdt=5t(2t2-1)3 now  using identity (a-b)3=a3-b3-3ab(a-b)

Q: Find the gradient Vf of the function f given the differential. df = (5x* + 1) ye*dx + x°e*dy Vf =

A: The differential of function f is given as- df=(5x4+1)yexdx+x5exdyWe need to find…

Q: x2 dy Find - for y = x dx -for y =x cos t?dt. sť dt. 2

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Q: Find the differential of the function. y = V 4 + cos(0) dy =

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Q: Find the differential dy of the given function. y = csc 5x dy dx

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Q: Find the differential dy of the given function. (Use "dx" for dx.) 6. y = 2/x +

A: Given:

Q: Let y = f(x), where f(x) = 3x+6/x+6 Find the differential of the function. dy =?

A:

Q: Find the differential dy of the given function. (Use "dx" for dx.) x + 2 y = 4х — 3

A:

Q: 3. x cos x dx

A:

Q: when

A:

Q: Find the differential dy of the given function. (Use "dx" for dx.) y = (x+1)/(3x-5)   dy=

A:

Q: Let y = e/3 Find the differential dy when x = 5 and dx 0.2 Find the differential dy when x 5 and dx…

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Q: 1. y = √2x +7 2. y = √7+√√3x + 1 3. y Arctan√1-x²

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Q: Find the general antiderivative of the given function. f(x)= sin (7y)+ cos (3y)

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Q: Q2: Suppose the electric potential at (x, y) is given by f(x, y) = 0.5 Ln(x² + y²) estimate the…

A: In this question, we have to find the error in f(x,y) and percent relative error for the given value…

Q: Find the value of dz and dz/ dy at the point A when x changes by (0.01) and y changes by (-0.01) xe…

A:

Q: dy dx || X x² + 100

A: We have given differential equation  dydx=xx2+100 dy=xx2+100dx Integrating both sides…

Q: Find the differential dy of the given function. (Use "dx" for dx.) y = 8x/2 = Ap dy

A:

Q: Find the differential of the function y = V1+ cos(0)

A: Find the differential of the function

Q: Find the change in y, Ay when x = 4 and Ax = 0.4 Find the differential dy when x = 4 and dæ = 0.4

A:

Q: Find the differential of the function. z = e-5x cos(9xt) dz = dx + dt

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Q: dv dv 5. Use the Chain Rule to find and ds v = ln (2.x + 3y), where x = s sin t, y =t cos s %3D

A: Here, Givenv=ln(2x+3y)∂v∂x=22x+3y∂v∂y=32x+3yAlso, x=s sin(t)∂x∂s=sin(t)∂x∂t=s cos(t)y=t…

Q: Find the differential dy of the given function. (Use "dx" for dx.) x + 2 y = 5x - 9 dy =

A:

Q: Let y=(x^2+2)^2 Find the differential dy when x =5 and dx =0.5 Find the differential dy when x=5 and…

A: a) Find dy for given equation.

Q: Find the differential of the function. Z = e cos(2nt) dz = dx + dt

A: Given,

Q: Determine the numerical value of dF of the function F(x, y) = e-3y cos(nx) given that X = 1, y =…

A:

Q: Find the differential of the function. Z = e-9x cos(2rt) dz = dx + dt %3D

A: The total differential of the function  is given by . So, to find , first we need to find the…

Q: r nosへSう'" ( メンン 2 COS(SIn (x))

A: Let, cos(sin-1x)=t⇒sin(sin-1x) 11-x2dx = dt⇒x11-x2dx = dt...(1)

Q: Find the differential of the function. w=2xyexz dw=(__)dx + (__)dy + (__)dz

A: W = 2 x y e xz dw  = 2 yexz  + 2 x y z e xz dx  dw  = 2 xe xz dy

Q: Find the antiderivatives |x In(x²) dx + sec? x dx CO X dx sin5

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Q: Find the antiderivative of the given derivative. ds = 14t(5t2 – 1)3 dt S=

A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.