Find the function r that satisfies the following conditions. r'() = (1,2t,5t"); r(1) = (3,5,4) r(t) = {OOD

Q: The function f defined by the rule f(z, y) = In(xy) increases fastest in the direction of T. F (1,…

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Q: Find fæ, fy, and fz. 4,5 f(x, y, 2) = 4z In (a*y° cos(5z))

A: We can answer all the three question as below.

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: -Find the D.f ofr (x, y) = (x² – y)' at Po(3, 1) with

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Q: Find the maximum rate of change of the following function at the given point. f(x, y, z) = x² + 5xz…

A: To Determine: find the maximum rate of change of the following function at the given point . Given:…

Q: Determine two functions, defined on the interval (−∞,∞)(−∞,∞), whose Wronskian is given by…

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Q: A:- Find the orthogonal trajectories for functions In -1) = - COS X +a y

A: The given family of curves is: lny-1y=-cos x+a ,            where a is an arbitrary constant.

Q: Differentiate f(x) with respect to g(x) of yx=xsiny

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Q: Use the second-derivative test to show that the function f(x, y) = x²eY – y²e* has a saddle point at…

A: A point (a,b) of function f(x,y) is said to be the saddle point if it is a critical point…

Q: Find the derivatie: F (+2 %3D (-t*+*z+)た =人

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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: (6) Find the orthogonal trajectories of the family of curves r= 2C cos 0, where C being parameter.

A: Consider the given curve. r=2Ccosθ          (1) Find the derivative of the given equation.…

Q: Obtain the orthogonal trajectories of xy = C and compute for the positive value of y at the point…

A: Solution

Q: 2. Find the gradient of the function f(r.y) In(r y²) at the point( 1, 1).

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Q: 8. What is the relationship between a and b so that F(x, y) = (ary, 3ax + bry) is source free?

A: That's easy. Have a great day!!!

Q: For the given function 9 = x-yz and 62 -(@C) at C= 3x?yi+ yz²j- xzk, Find 5yöz бубz point (1, – 2, –…

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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: Find the derivative of the given function at P. (3, 3, 3) in the direction of u = 3i + 4j f (x, y,…

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Q: For the function f(x, y) = (cos x)ey +v 1 + x + y. %3D Show the process of using the linearization…

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Q: Use a linear approximation to estimate f(0,1), given that y=f(X) is a differentiable  with f(0)=1…

A: Consider the given information

Q: Given : 6 (x, y, z) Compute the gradient = 3 6y³ z³ - 5 ex at PA (2,2,1-5) of G (x, y, z)

A: Given  G(x,y,z)=6y2z3-5e-x We have to find the gradient at the point PA(2,2,1.5)

Q: Find the linearization L(x)of the function at a .

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Q: Find the local linear approximation of f(x)= at 2+ x xo = 2, where Ax = x – 2. NOTE: Enter the exact…

A: while finding out the local linear approximation of any function f(x), what we do is to determine…

Q: If f(x,y,z) = z In(x²ycosz): then fz is

A: Here, the given function is: f(x,y,z)=z ln(x2ycos z) Using the properties of the natural logarithm:…

Q: 4/(A)Find the derivative of f(x, y) = xe + cosxy at the point (2,0) in the direction. дz (B)If Z =…

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Q: find the solution of following derivative by Runge-Kutta method f(x,y) = -2x3+ 12x2 - 20x + 8.5 let…

A: Consider an initial value problem dydx=f(x,y) with the initial condition yx0=y0. Then Runge-Kutta…

Q: Find an equation of the line tangent to f(x) = xcos x at x = -4. (Round coefficients to 3 decimal…

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Q: Eliminate the arbitrary constants a. x = -In t, y = at + bt?

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Q: What does it mean for the differentiability of a function if only one of the Cauchy-Reimann…

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Q: What does it mean for the differentiability of a function if the Cauchy-Reimann equations (Ux = Vy…

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Q: Find the gradient of the function at the given poin In(x² - y) -2, (3,8) X Vz(3, 8) = Z =

A: We are asked to find the gradient of the function.

Q: Find the local linear approximation L (x) of the function f(x) = 5 – x² at =2.

A: To find the linear approximation of given function.

Q: Find the linearization L(x) of the function at a. f(x) = sin(x), a =. 3 L(x) =

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Q: 1. Integrate the function f(x, y) = x – y over the triangle T with vertices (0,0), (1,0), and (1,2).

A: Given triangular region is bound by the vertices 0,0, 1,0 and 1,2. The sides of the given triangular…

Q: Let f(1,y) = (r+ay°,r²y°,2r + by), g(u, v,w) = (3u² + bv² + w°, uvw). Find the derivative of…

A: Let f(x, y)=x3+ay2, x2y3, 2x+by,  gu, v, w=3u2+bv2+w3, uvw. We need to find the derivative of fgu,…

Q: -2 In(x) Consider the function f(x, y) 3y

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Q: Q, Frd the donain of H fallowing function: fa) = 5x -3x-4

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Q: Find the best linear approximation to f(x) = ex on the interval [-1,1]

A: We have to find the best linear approximation of f(x)=ex on the interval -1,1.

Q: Find the linearization L(x) of the function at a. f(x) = sin(x), a = 3 L(x)

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Q: Verify Young's Theorem f(x,y) = e(2x+y) In(xy)

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Q: Suppose f(x, y)= g(x)h(y), where g and h are continuously differentiable functions of one variable…

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Q: Suppose z = ƒ(x, y), where x and y are functions of t. How many dependent, intermediate, and…

A: It is observed that z=fx,y is function of x and y.

Q: Suppose that f(0) = 1, ƒ(0.5) = 2.5, f(1) = 2, and f(0.25) = f (0.75) = a. Using trapezoidal rule…

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Q: 3. Let f(x, y) = In 2x + 4y, find the directional derivative of f(x, y) in the direction of at the…

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Q: Determine f„ (0, T, 1), fy(0, , 1), f¿(0, r, 1) given the function z sin(3xz+ y²)

A: The given function,        zsin3xz+y2

Q: Find the linear approximation of f(x)=(1+x)3 at x=0. Using this approximation to estimate (1.01)3…

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Q: Find the linearization of the function f (x) = =° at z = 1. L (1) = Using this linearlization, ƒ…

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Q: (b) Show that the function defined by xy √√√²+y² f(x, y) 0 if (x, y) = (0,0) is not differentiable…

A: We have to show that the function defined by…

Q: Consider the function f(x,y) = (3x^2 + bx)(2y^2+dy) where b and d are non-zero constants. Determine…

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Q: Consider the function: u = 2 ln /x² + y² Show that uzz + Uyy = 0. %3D

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