Show that (t) =| 2 3t is the fundar

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Q: 8. Find the orthogonal trajectories of vy = cx

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Q: Find the linearization of x+1 f(x) = 2 – dt 1 + t“ at x = 1.

A: Given function is

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A: Here we use the definition of boundedness of a linear operator.

Q: Calculate the linearization L of f(x) : 5e* at x = 1. x2 Express your answer in terms of e and x.

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Q: 8. Find the orthogonal trajectories of Vy = cx

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

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Q: 2ys = Cx

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Q: Show that E [x(t)] = 0. %3D

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Q: Find the Tians Farm F(s) = "suy (27>1>0) (1 – s)(1 – e **) 3) f(1) = e',

A: Given problem:- Find laplace transformation of f(t) =et (0&lt;t&lt;2π)

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Q: [1] Determine the orthogonal trajectories of y(1+2x?)=ax.

A: The given equation is:y1+2x2=axy=ax1+2x2              ..............(1)

Q: Find the orthogonal trajectories of the given family of curves x - 4y c.

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Q: Let x~ exp (A) Show that T=s Xi is sufficiency Statistic.

A: Generally we use factorization theorem to obtain the sufficient statistic.

Q: Find the linear approximation L (x) to ƒ (x) = xcosx at a = T.

A: Given that, f(x) = x cosx and we have to find linear approximation L(x) at a = π

Q: 7  please answer, type the solution if you can please. or write clearly

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Q: 2. Show that the function u p(xy) + Vry (y/x) provides the equation = 0.

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Q: Let A = {(x,y) = RXR; 0<max{|x-3], ly- 2|}<1}, then: *

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Q: Find the d. c. of from definition. Vx

A: As per the question we have to find the derivative of the function : f(x) = 1/√x Using the limit…

Q: The function f(x) = Ei-1 Cix;| is piecewise linear and convex. True O False

A: Step:- 1 Convex piece-wise Linear: - A function f: ℝn→ℝis a convex piece-wise linear if there exist…

Q: Let f (x,y) =In Then f „(1, – 1) =... 3x²+ 4y3

A: This is a problem of partial.

Q: Find the orthogonal trajectories of the family y = 1 - sec?r + C 4

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Q: 4. Use the linearization of f(x, y) Vx + 2y to approximate f(3.01,2

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Q: of of and ду Find f(x,y) = Vx + 3y?

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Q: Find f, and f,. f(x, y) = 13x In xy

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Q: If A(x)= f(t)dt is increasing on [0,10], then f(x) must be increasing on [0,10].

A: Given,A(x)=∫0x f(t) dt

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Q: Find the orthogonal trajectories of the family of 1 curves Y= X + k

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Q: Find f(t). s(s + 1).

A: L-1[F(s−a)]=eatf(t) From first shifting property, L{e^(at)*F(t)} = f(s-a)…

Q: Let f(x, y) = ln (3x + y2). Show that fxy = fyx

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

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Q: Find the linearization L(x)of f(x)at x = a where f(x) = Vx² + 9 at a = –4

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Q: 2: Find the orthogonal trajectories of xy=C.

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Q: If g(x)=- A B d- ſ ^ [e' − In(2t + 1) ]dt, find g*'(x) . dx -2 2 (2x + 1)² 4 et + (2x + 1)²…

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Q: d. d rsinx 2t3 -t dt dx 4

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Q: --—-^[e'-In(2t+1)]dt, find g''(x) . dx -2 If g (x) = (A) (В Ce*- D 4 (2x + 1)² e* - In (2x + 1) 2…

A: We have to solve integral

Q: Find the orthogonal trajectories of the family of x² – y? = cx = CX -

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Q: 3t – 2 dt t + 1

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Q: 8. Find the orthogonal trajectories of y = cx CX

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Q: if the implicit function is x3=at2, find the d2x/dt2

A: if the implicit function is x3=at2, find the d2x/dt2

Q: Find the orthogonal trajectories of У — сх CX

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Q: Suppose that , g(t) dt = v2 g(r) dr V2 b [-g(x)] dx а. -3

A: Given: ∫-30g(t)dt=2. The objective is to find, ∫-30-g(x)dx ∫-30g(r)dr2

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A: Explanation: The Linear Approximation should be a line that can substitute (in a narrow interval)…

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Q: Find the linearization L(x) of y=e10xln(x) at a=1

A: y=e10xln(x)  The linearization L(x) of a function f(x) at x = a is, Now  Now differentiating given…

Q: 8. Find the orthogonal trajectories of CX

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Q: Use the Quotient Rule to compute the following: t2 + 1 at t = -2 dt \ t2

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