Find the orthogonal trajectories of the famil y of curves x'yxy=c where cis constant

Q: Compute the indicated derivative using the chain rule. dy x = 1 – t/3, y = 8t – 1; dy %3D

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Q: Find the linearization of the function f(x,y) = ln(x3y6) at the point (x0,y0) = (4, 3). Leave all…

A: Given fx,y=lnx3y6     at (4, 3) The linear approximation in 2 variables is given by Lx, y=fa,…

Q: Obtain the gradient to a curve with parametnic equations given by and y= X= In 2 2t when t-1

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Q: Find the derivative of y with respect to t. y= sin 1(10t) dy dt %3D

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Q: Find the maximum rate of change of the function f(x, y) : 4y4 at the point (1,3)

A: We will solve the problem

Q: Consider f(x, y) =(ax² + by²). Based on the second derivative test, what are the conditions…

A: Answer

Q: Suppose f(x,y)=xex. At the point (2,0), in what direction is the directional derivative maximized? |

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Q: Find the maximum rate of change of f(x,y) =x²y+ /y at the point (1,1). In what direction does it…

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Q: Find the derivative of y = = Ve-5t +1 dy dt ||

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Q: Compute the indicated derivative using the chain rule. dy x = 5 + 3t, y = -8t; dx dy %3D dx

A: We have to find the indicated derivative by using chain rule: x=5+3t, y=-8t Differentiating first…

Q: Is there a smooth (continuously differentiable) curve y f(x) whose length over the interval 0sxsa is…

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Q: 2. Find a function f(x, y) which is NOT linear in either a or y and for which the tangent plane at…

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Q: Find the orthogonal trajectories of the family of curves: y = k (csc x + cotx) Ⓒy² = 2 (C- cos x) O…

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Q: Consider the following information fz(x, y) = 2xy - 2r³ and f₁(x, y) = x² + y² – 6. Use the Second…

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Q: Find the maximum rate of change of f (x, y) = xln /x2 + y2 at (1,2) and direction in which it…

A: To find the maximum rate of change of fx,y=xlnx2+y2 at 1,2 and direction in which it occurs.  First,…

Q: Find the point where the CAUCHY- RIEMANN equation is satisied for the function f(2) =xy+Xyi

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Q: 2. Find the equation of the tangent plane to f(x,y) = sin(x² +y) when x = 0, y = T. 3 and r - cost

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Q: 2.Evaluate the total derivative of u with respect to x for u = 4x4+3y² + 3z² when y = sinx and z =…

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Q: Find the gradient of a normal line to the parabola y=x^2+5x-9 at the point (1,1)

A: In this question, the concept of slope is applied. Slope A line's slope or gradient is a number that…

Q: What is the linearization L(x, y) of a function f (x, y) at a point (a, b)? How is L(x, y) connected…

A: Linearization L(x,y) of a function f(x,y) is given by the formula

Q: Calculate the derivative 10z d dz In (t)dt using Part 2 of the Fundamental Theorem of Calculus.

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Q: Find the derivative. (Hint: en a = x) %3D y =S 4 In x et dt O * - 1 4x3

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Q: Find the set of orthogonal trajectories for r = VA sin (2e)

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Q: Find the maximum rate of change of f at the given point and the direction in which it occurs…

A: Consider the function: fx,y,z=xlnyz Differentiating with respect to “x” then,…

Q: Find the total derivative of the function f(x, y, z) =+z In (2x+1)+sin (xy) xz

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Q: Find the maxcimum rate of change of f at the given point and the direction in which it occurs. F(x,…

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Q: Find the differential d5y of the function y=lnx2.

A: y = lnx2 = 2lnx

Q: What is the difference between the linearization, L(x), of f at a, and the linear approximation (or…

A: Given question:- What is the difference between the linearization, L(x), of f at a, and the linear…

Q: 2. Use second order derivative to derive the acceleration, a for an object that falls where its…

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Q: Find the orthogonal trajectories of the family of curves: y = k (csc x + cotx) Ⓒy²= 2 (C- cos x) O y…

A: This question is related to differential equations, we will solve it using given information.

Q: Let (x, y) = 3y² - 2y – 3x² + 6xy. a. Find the equation of the tangent plane at the point (1, -1).…

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Q: In(3x² – 2y + 4z³); x = t², y = t³ , z =t-l. Find the maximum derivative the function f(x, y) = x² –…

A: Given that w=ln3x2-2y+4z3 The objective is to find dwdt By chain rule,…

Q: Use implicit differentiation to find dz/ yz = 5 In(x + z) az dz dy II

A: The given equation is yz=5lnx+z Differentiate the given equation partially with respect to x.…

Q: f (x, y) = 3x^3 −9x+9xy^2. Use the second derivative test to classify the critical point (1,0) as a…

A: Recall: second derivative test : (i)  Firstly find critical points . i.e, fx(x,y) =0 and…

Q: 6. y = C Sin x 7. y = cx?

A: To determine the equation of the orthogonal trajectories of the following families curves: y=Csinx…

Q: Use implicit differentiation to find az/Əx and əz/əy. e4z = xyz Əz Əx az %3D ay II

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Q: Find the equation of the tangent plane to z = ln(2x + y) at −1,3

A: Find the equation of the tangent plane to z = ln(2x + y) at −1,3

Q: Find the maximum rate of change of f(x, y, z) = tan(2x + 2y + 3z) at the point (−9, 6, 2) and the…

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Q: Calculate the second-order partial derivative of f(x.v) =sin(x³v?) with respect to x and y, that is,…

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Q: Find the derivative of g(x) = |. •r In z Vt2 +t+1 dt

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Q: Find the derivative of the function. y = (3t – 1)(6t – 6) -1 dy dt II

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Q: What is the rate of increase of the scalar function f(x,y,z) = sin (πx/3) sin (πy/2) e^-2z from the…

A: See the attachment

Q: Repeat Exercise 60, except with these derivative boundary conditions: y'(0) = 0, y'(π) = 1. In part…

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Q: Compute the derivative y = dy %3D dt 2t - 7 y = 7t- 3

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Q: Find the gradient of the tangent to the curve xy“ + y+ ( log_(x – 2))² = 14 at the point (3, 2).

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Q: Confirm the approximations by using the linear approximation at x = 0

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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.