t = 1, a particle is located at position (x, y) = (5, 4). If it moves in the velocity field F(x, y) = , find its approximate location at time t = 1.0

Q: A cylindrical shell has a thickness of 0.2 cm. Using differentials, approximate the volume of the…

A: The volume of the cylindrical shell is given by V=2πrh∆r, where ∆r is the thickness of the shell.…

Q: Show that the differential form in the integral is exact. Then evaluate the integral. (1,2,3) Jazy…

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Q: Find the Integration of: fn (3sint + esin t) cost dt In 3

A: Given that, ⇒                   y =∫π2π( 3sint +esint) costln3dt⇒                     find the value…

Q: The base radius and height of a right circular cone are measured as 10 cm and 25 cm, respectively,…

A: Given formula for the volume of the cone is V=πr2h3 Now, the total differential of V can be…

Q: The linear approximation at æ = 0 to sin(2z) is A + Bx where A is:| Previev and where B is: |…

A:

Q: Suppose a force of 40N is required to stretch and hold a spring 0.1m from its equilibrium position.…

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Q: Resolver por transformada de laplace  Y"+4y=cosx.  Y(0)=1  y'(0)=1

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Q: Find both first partial derivatives. sinh(5x + 4y) az %3D dz %3D ду

A: Explanation of the answer is as follows

Q: The length and width of a rectangle are measured with errors of at most 3% and 5%, respectively. Use…

A: Let the length and width of a rectangle are L and W respectively. Now, The length and width of a…

Q: te dt.

A:

Q: Simplify down to a single integral in terms of . .3 /9-x² 63–42²–4z² Volume = 1 dy dz dx = Σ da.…

A: ∫-33∫-9-x29-x2y3x2+3z263-4x2-4z2dzdx

Q: The dimensions of a closed rectangular box are measured as 93 cm, 66 cm, and 50 cm, respectively,…

A: Given,           The dimensions of a closed rectangular box are measured as 93 cm, 66 cm…

Q: A Korean corn dog is a cylindrical piece of hotdog, rice cake, or mozzarella cheese, evenly coated…

A: Given: Calculate how much larger (in cm2) the cross-sectional area of the XXL item C is compared to…

Q: tany = C secx

A: The question clearly asks us to find the family of orthogonal trajectories of the given family.…

Q: The equation of the upper semicircle centered at the origin with radius R in parametric form is…

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Q: The forces of the human gastrocnemius tendon during traction and during recoil can be approximated…

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Q: Pind the ualue of e is an integrating facko of ly-y')+xy'so

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Q: 5. Evaluate S (tan(2y) + cot(2y))² dy using integration by algebraic substitution.

A:

Q: Find the total differential w = x2yz2 + sin yz

A: Partially differentiate w = x2yz2 + sin yz with respect to x and keep y and z as constants.…

Q: The edge of a cube was found to be 30 cm with a possible error in measurement of 0.1 cm. Use…

A: Given: The edge of a cube, x=30 cm The error in measurement, ∆x=0.1 cm

Q: A particle moves along the x-axis with velocity dx/dt = ƒ(x). Show that the particle’s acceleration…

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Q: Find both first partial derivatives. z = sinh(7x + 16y) az ax az ду

A: From the given problem: z=sinh7x+16y As we know that: The chain rule: fgx'=f'gx·g'x The Power law:…

Q: Suppose the side length of a cube is measured to be 5 cm with an accuracy of 0.1 cm. a. Use…

A: The measurement of the side length is accurate to within 0.1 cm. Therefore,  -0.1≤dx≤0.1  The volume…

Q: find the soution of' the differential eq. System X= 3X+44 9=X+3y %3D

A: Given differential equations are                                     dxdt=3x+4y,dydt=x+3y…

Q: A manufacturer produces a triangular lamina with a standard base and height of 30 cm and 12 cm,…

A: we have been given the measurements of a triangle a base = 30 cm and a height =12 cm  area of the…

Q: Let u=sinx and the integrand will lead to integration by partial fraction

A: use substitution method for solving the  integral

Q: Find the partial derivative of f(x,y) with respect to y at the point (3,2) f(x,y) = ln(x^2y-xy^2)

A: A partial derivative of a function of several variables is its derivative with respect to one of…

Q: he integra = 3/2 is dz Z-2

A:

Q: Q₁) Find $dz 1. around unit circle of radius 1 and center at (0, 0) counterclockwise. 2. By using…

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Q: Find the first partial derivative of w = In(1 + )at (2,0, – 1).

A:

Q: Find the area of a triangle bounded by lines y=2x and x=1 by double integration

A: Given region, y=2x        ...(1)x = 1        ...(2) Substitute the value of x = 1 in (1), y = 2 So…

Q: THE AREA BETWEEN THE CURVES 4 y = x²³² AND y ²³ = 4X IS REVOLED 2 ABOUT THE LINE X= -1. SOLVE FOR…

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Q: 46. s(х, у) tan (y/x) -1 =

A:

Q: A Korean corn dog is a cylindrical piece of hotdog, rice cake, or mozzarella cheese, evenly coated…

A: We will use total derivative to find change  If f is a function of x and y  ∆f=∆x×∂f∂x+∆y×∂f∂y

Q: Find the limits of integration in cylindrical

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Q: I Eliminate the arbitrary constants 1. X = y=at + bt² - Int,

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Q: Suppose f(x, y, z) = xy cos z.Compute the partial derivative of f with respect to the variable y at…

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Q: Find both first partial derivatives. z = sinh(7x + 5y) az ax az ду || ||

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Q: What can you conclude about a real function f(x,y) that has continuous partial derivatives at a…

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Q: Find the area of a triangle bounded by lines y=2x and x=1 by single integration

A: A definite integral can be used to compute area bounded by curves. If there are two curves f,g over…

Q: Evalute Sofy ex* dxdy by first reversing the order ex² 3y integration.

A:

Q: Find the value of dx at the point (1,1,1) if the equation 6xy + z"x-2yz = 5 defines z as a function…

A: Given: (x,y,z)=(1,1,1) and z=6xy+z4x-2yz-5=0

Q: v = exy In(x +y)

A:

Q: but its partial derivatives are not continuous at (0,0).

A:

Q: What is the (a). general solution to xydx-(x+2) dy=0? (b) integrate.

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Q: 2. Suppose that a particle is moving along the curve 4x2 + 16y? = 32. When it reaches the point (2,…

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Q: What is the Fourier transform of the one-dimensional rect function rect(x) = 1, for |x| |x|…

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Q: Q10.a) Find rsinx if tnx Jt +5 dt + siny = x – x²cosy

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Q: Let y=sqrtX. Find dy/dt when x=4 and dx/dt=3

A: →Use chain rule of differentiation.→dxndx = n xn-1     When n = 12         dx12dx = 12 x12-1…

Q: Find the differential equation of the family of spheres of radius r with Centre on the xy-plane

A: General form of the equation of the sphere with radius r and center on the xy plane is given by…

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.