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![Exercises
In Exercises 1-8, find a point c satisfying the conclusion of the MVT
for the given function and interval.
1. y=x-¹, [2, 8]
3. y = cos x sinx, [0, 2π]
5. y = x³, [4, 5]
7. y e-2x, [0, 3]
2. y = √√√x, [9, 25]
[1,4]
X
x + 2'
6. y = x lnx,
8. y
4. y =
[1,2]
ex-x, [-1, 1]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F48a7e361-4af0-4f56-bb6f-d3591bf986f7%2F8db344ea-43f0-49d6-8dd9-c38cceb9227a%2Fgqytbie_processed.jpeg&w=3840&q=75)
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- f 1 (x) = x and f2 (x) = sin (x) sin Wronskian functions that are linearly independent show using.In Exercises 23–26, find ƒx , ƒy , and ƒz . 23. ƒ(x, y, z) = e^-(x2+y2+z2) 24. ƒ(x, y, z) = e^(-xyz) 25. ƒ(x, y, z) = tanh (x + 2y + 3z) 26. ƒ(x, y, z) = sinh (xy - z^2)How do we find the linearization of g(x, y) = tan−1(xy2) at the point (1, 1). and use linearization to estimate g(1.08, 1.037). thank you.
- Use field II to sketch the graphs of the solutions that satisfythe given initial conditions. a) y(0) = 1 b) y(0) = 2 c)y(0) = -112 help use variation of parameters to finda general solution to the differntial equation given the function y1 and y2 are linearly independent solutions to the corresponding homogenous equation for t>04 a. Consider the i.v.p x' = t^(2) + cos(x), x(0) = 0. Verify that the hypothesis of Cauchy Picard theorem for a suitable domain D. b. Then estimate the interval of existence of the solution.
- 4 a. Consider the i.v.p x' = t^(2) + cos(x), x(0) = 0. Verify that the hypothesis of Cauchy Picard theorem for a suitable domain D. b. Then estimate the interval of existence of the solution. Use applied analysis and then I want the solution handwritten.What does it mean for the differentiability of a function if only one of the Cauchy-Reimann equations (Ux = Vy and Vx = -Uy) holds?Find the linearization L(x) of f(x) at x=a f(x)= x+1/x a=3 show all work
- We want to estimate f(1.01 , 0.97) for the function f(x,y)= √(4 - x2 - y2). For this, we can use an appropriate linearization of the function f(x,y).Then Fx (1,1) = ? and Fy (1,1) = ? therefore we can estimate the mentioned value obtaining an answer of f( 1.01 , 0.97) ≈ L( 1.01, 0.97) =Let X, Y ~ N(0, 1) be independent. Find the moment generating function of X2 + Y2. Hint: If X, Y are indepenent, then X2 and Y2 are independent.A mass m moves along the x-axis subject to an attractive force given by 19mx/2 and a retarding force given by , where x is its distance from the origin and is a constant. A driving force given by , where A is a constant, is applied to the particle along the x-axis. Write down the equation of motion. What value of results in steady-state oscillations about the origin with maximum amplitude? What is the maximum amplitude? what is the Q value?