w= Pcxiy,Z) = In (x+y+2) ,x= cost, and z = 4VE %3D 2X = y= Sint >use ch ain rule to Rind du in terms ofE

Q: If we use Trapezoidal rule to approximate * f(x)dx then find the value of x2, where n= 6 Select one:…

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Q: 15 estimate, root of fa) =x²-7.

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Q: Use the clerivative rules to tind the deriVative of y. y=(x² + y> x²? (x-1)s y= (4x-1)3 2x+)

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Q: Approximate  ∫21ex^2dx using the Trapazoidal Rule with n=5

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Q: Use an appropriate local linear approximation to estimate the value (2.03)^3

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Q: What is the average velocity, given s= (3t^2+5) ft and t changes from 2s to 3s

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Q: DO NOT include spaces in between characters. * 7 Given y=(3x +6)| 2x– Find the value y' at x = 4

A: Given:       y=3x2+62x-14 Differentiating on both sides with respect to x.      y'=ddx3x2+62x-14…

Q: let G={2nEIJ.] show that (I, +) = (G₁.)

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Q: 4. Use differential to estimate v15. (3 points total)

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Q: Find the image of the following lines/curves y=(1/x) under the mapping f(z) = z^2. If possible,…

A: Given y=1x fz=z2  we know z = x+iy

Q: 10. Evaluate: 0 x³ dx Ĵ 47 ₁(2-x²)²

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Q: u= e^ if taken dx fluldu= glultc %3D respectively f4)=7,841=? as

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Q: Is F =Y. x> x+y? conservative

A: Proceed as shown

Q: Estimate (1.02) V0.99 using a local linear approxima

A: Here we have to use the linear approximation.

Q: Use the Quadrature Rule Calculate I = S e2x dx using the 3-point Gaussian Quadrature method.

A: Given integral is I=∫03e2xdx

Q: Data was collected from twenty-two mountain ash trees of different sizes. A graph of the data values…

A: Data was collected from twenty-two mountain ash trees of different sizes. A graph of the data values…

Q: Find the derivative of y=fG)= Jx3 + x2 * Do not use product quotient rule. or

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Q: do implicit diff for thi with respect to x (xy)^(1/2) = 4 + x^(2)y

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Q: Which derivative rule is used to derive the Integration by Parts formula?

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Q: Write down a formula for ∂z/∂y if z is defined implicitly as a function of x and y by the equation…

A: The given equation is yz=e3x+z.

Q: rconh(3x+1) - 5t +ldt f(x)= sinh³

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Q: how that Q CQ(2^(¹/4), i) is normal. Again, what is conclusion?

A: We have given that  Q is subset of Q(2^(1/4),i) is normal so it is about conclusion.

Q: y=3x^(3/2) on [2,4] find arclength

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Q: got y=x^3In(x), but it says to write it in y=mx+b form so im not sure if that's supposed to make it…

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Q: Use implicit clifteren tra fion to find * for the fol llving x*y+ 3xy-x = 3

A: The given equation is x2y+3xy3-x=3 To find: dydx

Q: Use the IVT to prove thatx^2+ lnx =1/2 has a solution.

A: Use the IVT to prove thatx^2+ lnx =1/2 has a solution.

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.