1. A functionz = f(x, y) is given. Give the indicated approximation using the total differential. Ax, y) = Vx2 + y. Approximate f(2, 95, 7.1) knowing (3, 7) = 4.

Q: xyz 1+x*+y*+z* where x, y and Suppose that the height of a hill above sea level is given by S(x,y,z)…

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Q: -4 Chapter 13 / Partial Derivatives f(x, y) = x2 + 2ry- 4x; P(1, 2), Q(1.01, 2.04)

A: Explained below

Q: 2. Find the gradient of the function f(x, y) = ln(x² + y²) at the point(1, 1).

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

Q: 1 E = 4. UA (10-3) 2(1+v) k UE

A: Just shift epsilon to right side and (1+v) to left side.

Q: Q4: Find the derivative of the function at Po in the direction of A 3) f(x, y, z) = xy+ yz + xz,…

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Q: Q10. For the function f(x, y) = x³e3y find the maximum value of its directional derivative at the…

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Q: IV. Find of the following. dx 1. x-(1-2y +3y2) y-2 | 2. x = (3 + y² Xy +1)³ 3. = V1-t *ly=1 +t %3D

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Q: Find the maximum rate of change of the the function 80 f(x, y, z) = 1+g² + 2y? + 3z² %3D at the…

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Q: Q1. Let f(x, y) = x²y + x + y² +3. (a). Find f(x, y). (b). Find dy

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Q: Find a linear approximation to f(x,y) : = (x? + y²)e-(x²+y*). At (0, 0), and use it to approximate…

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Q: Find the approximate change in z when the point (x, y) changes from (4, 9) to (3.98, 8.89). (Round…

A: To find the approximate change in z when the point (x, y) changes from (4, 9) to (3.98, 8.89).

Q: Suppose y = (x² + 5)³. (a) Find the differential: dy dx. (b) Compute the differential when x dx 2…

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Q: Given the function z = I a. Find the directional derivative of z at (2, 6) in the direction making…

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Q: 4. y2 +2xy 4, find y" Ans. y" = (x+y)

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Q: The pressure, volume and temperature of an ideal gas are related by the equation 8.31T P(T,V) = V…

A: Given, P(T,V)=(8.31T)/V At centre V=12litre and T=310k

Q: 11. Let f(x, y) = 2x²y. From which of the given (x, y) points does ƒ have the largest direc- tional…

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Q: determine the most general function M(x, y) or N(x, y) so that equation is exact.

A: We have to find M(x, y) Or N(x, y).

Q: Copy the slope fields (mentioned in the Attachment) and sketch in some of the solution curves. y' =…

A: Given: y'=y(y+1)(y-1)

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.