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Q: 3.2.10 Example: By method of contour integration, prove that dx = t /4 (1+ x }

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Q: y(t) – S y(t)sen2(t – t)dt = sen2t

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Q: dy = 2t°y + y + 2t + 1. Show your work and explain thoroughly, when appropriate. dt Determine the…

A: To find the general solution of the given differential equation, first we separate the variables and…

Q: The value of local acceleration in the x direction for flOW with all wrong u = 2(1 + t) is given by…

A: Given that  u=2(1+t)  To find the local acceleration in the x direction of flow

Q: 2x + 7x +3. If Ax = 0.3 at x = 4, use linear Let y approximation to estimate Ay %3D %3D %3D Ay =

A: Given y=2x2+7x+3 if ∆x=0.3 at x=4 we have to approximate ∆y using linear approximation.

Q: 5. f'(x) dx = Choose... 6. cosh t dt = Choose...

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Q: da Find at z = 4 if y = 4z² - 1 and dt da dt 11 > Next Question dy dt = -5. 11

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Q: dy at t = a where dt Find f(1+ vu), u = 2-x? and f'(2) = -3.Find dy when x = 1. dx 8. Let y ||

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Q: Differentiate: y(x) along the curve xy =ex Show all working out.

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Q: Tangent to the curve z2 = 2xy + x2 , z = 3 , at the point ( 1, 4, 3) %3|

A: For a surface of the form: f(x, y, z)=0, the equation of the tangent at x0, y0, z0 is defined as…

Q: Q4:- Find the derivative of the function at Po in the direction of the vector AC. f(x, y, z) = x² +…

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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: Assume that x = x(t) and y=y(t). Let y = x³ +5 and dt Find dt dy dt when x = 3. (Simplify your…

A: Here is the solution:

Q: Gixen dw wt 3y x dt dy +2X +3 x Find the gencral oludtii, usri eign.

A: Write the given system into matrix equation as follows.

Q: Resuelve la ecuación integro-diferencial y'(t) = cos t + y(7) cos(t - 7) dT, y(0) = 1 %3D

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Q: dy 4. Let ry = 1 and dt da Find when x dt = 2.

A: By using derivative of function

Q: Solve ux – uy +yu = 0, where u is a function of x and y. %3D

A: Given: ux-uy+yu=0. The objective is to solve u, where u is a function of x and y.

Q: 5x + 6x + 2. If Ax = 0.2 at x = 1, Let y = approximation to estimate Ay use linear Ay =

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Q: = y – 2², dt dy = y - ar. - у — dt For parameter a, classify the equilibrium points when a>5

A: Both the equilibrium points (0, 0) and (a, a2) are saddles.   Explanation: Let   First, we find the…

Q: Find the linearization of the function a) z = cos(sin y – x); at (-2,0) and use it to approximate…

A: Suppose f(x,y) be a differentiable function at (a,b). Then linearization of f(x,y) at (a,b) is given…

Q: 1, use 2x2 + 3x + 2. If Ax linear approximation to estimate Ay Let y 0.4 at x = Ay 2

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Q: Xyz f(x.y.z) = function is given dt P(2,t,) in point fax + fy + f2z colculate.

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Q: (2) Let f(x, y, z) = xy + yz + x²z². What is the maximum rate of change of f at (1,2, 3)?

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Q: of Let f (x,y)=tanh-1(x-y) with x=e" and y= usinh (t). Then the value of evaluated at the point dt…

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Q: 10. The sides of the rectangle at right increase in such a way that the instant when x = 4 and y =…

A: We need to find the value of dxdt, given that dzdt=1,dxdt=3dydt,x=4,y=3

Q: Integrate f(x,y) = x-5y over the curve C: x +y = 64 in the first quadrant from (0,8) to (V32,/32).…

A: Formula Used:Line integral ∫Cf(x, y) ds=∫abf(x(t), y(t)) dxdt2+dydt2dt

Q: Solve dy = ytan t, dt using separation of variables given the inital condition y(0) = 15. Assume the…

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Q: uestion 4 Assume that all variables are the function of t. If 5x2 - 4y3+3y=7 and dy/dt =6 when x-13…

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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: 4x + 2x + 3. If Ax 0.1 at x = 5, use Let y = linear approximation to estimate Ay Ay 2

A: A detailed solution is given below

Q: 2 - What is the directional derivative of the function f(x,y,z) = x3 - 2xy +z at point Ao= (1,1,0)…

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Q: 0Y Find the direction derivative of fcxy)=xy at the paint (2,1), by the dirction of v- i-j

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Q: Assume that x and y are differentiable functions of t. Find  dx/dt given that x= -3 , y= -2 , and…

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Q: g(x) = | f(t)dt- %3D

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Find dy/dt when x=4 and dx/dt=-3, given that x^3+y^3=72

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Q: Fx to find dy Assuming - 7x - 9y2 - 2xy = 0 defines y as a differentiable function of x, use the…

A: To find the derivative using the theorem

Q: 22. Find when t=, where x a(t + sint), y= a(I-cost) and a is a constant %3D

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Q: (2^)u sec (VTt) 2V7t (a) y= tan dy: dt 5- v2 (b) y = 5 + v2 dy = -5- 2iv 5 -V-5-2iv5 %3D Need Help?…

A: Both the parts are given below.

Q: A particle is moving along the curve y=x- 2 where x and y are functions of t. Find dx/dt if dy/dt =…

A: From the given problem:   y2=x3-2 ....(1)dydt=4.   Now differentiate the function with respect to x.…

Q: The maximum directional derivative of f (x, y, z) = x² sin(zy) – yx + 10 | at (-1, 2, 0) is

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Q: Tangent to the curve z2 2xy + x² , z = 3 , at the point ( 1, 4 , 3 )

A: Consider the curve, z2=2xy+x2 ⇒x2+2xy-z2=0

Q: dz Suppose that z = f(x, y) is differentiable at the point (8, 16) with f,(8, 16) = 3 and f, (8, 16)…

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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: Find the linearization of f (x) = xe¯* at a = 0. (Hint: Remember thne product rule.)

A: Given : fx = xe-x2

Q: Tangent to the curve z2 = 2xy + x² , z = 3 , at the point ( 1, 4 , 3

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Q: 2s+3 13. F(s) = s2–5

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Q: A) Use the chain rule to find dt where wxty,x = sint + cost y cost- sint.

A: We will use chain rule to find the answer :)

Minimization

In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in terms of global or local range. The definition of minimization in the thesaurus is the process of reducing something to a small amount, value, or position. Minimization (noun) is an instance of belittling or disparagement.

Maxima and Minima

The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.

Derivatives

A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which one would be easier? Walking on the road would be much easier than climbing a mountain.  

Concavity

In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the first derivative test and second derivative test to understand the concave behavior of the function.