Let u(x, t) be the solution of the Cauchy problem 9Uxx :0, u(x,0) = f(x) = Find u(0,1). Utt [1 |x|≤ 2, { 0 x > 2, -∞0 ut (x,0) = g(x) = 1 0 x ≤ 2. x > 2.

Q: Suppose f(): R" → R, G(.) : R" → R", and H(.) : R" → R² are functions. Consider the optimization…

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Q: 5. Find the on the interval [0, 4]

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Q: 8. Sketch a graph of f(x) that satisfies all of the following conditions: i) f(x) is continuous and…

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Q: 1- 4x ,0<x<1 Let f(x) = [x - 2x].1sx<2 Then discuss the differentiability of f(x) in(0, 2).Here [.]…

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Q: A function f(z) which is analytic in the disc |z| a > 0. Show then that |f'(0)| < (const.)a²b and…

A: Given, fz≤2a3+b3z3 Then, finding the optimal constant of the given function.

Q: 4. Show that: f(x) = 2²²₁ x+1 f'(x) = = 4x (1+x²)(1+x)(1-x) (x¹+1)² a. What are the critical points…

A: Given functionL:- fx=2x2x4+1

Q: For a certain function, f'(x) = 0 and f' (x) > 0 for -1 < x < 2. Which statement is not true? a)…

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Q: Find the absolute Minimum of f (x)= 12.1 [+ 4x - x^2 on [ 0, 5 (äbäi 1) * 16 12 20 7

A: Given  f(x)=12+4x-x2      0,5 f'(x)=ddx(12+4x-x2)=4-2x f'(x)=0 ⇒4-2x=0⇒2x=4  ⇒x=2 Critical point…

Q: False. For example, the maximum off (x) = x 2 + 1 on [l, 2] is 5, occurring at x = 2, but f' (2) #…

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Q: 5) Find the absolute maximum and minimum values of f(x,y)=x²-4y². on the rectangle D={(x,y) e…

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Q: . Let consider f(x) = x³-3x on the interval [-1,2]. (a) Execute first 2 iterations of Golden Section…

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Q: 2. Given f(x) = a) Find the critical numbers of f in the open interval (0, 2). b) Find the absolute…

A: By using Second Derivative Test find Critical Points and Absolute Extreme Values.

Q: 6. Find all critical numbers and use the Second Derivative Test to determine all local extrema. a)…

A: for part a see 2nd step. for part b see 3rd step.

Q: Consider the following function f(x)=2(x+1)2 in the interval [-2, 3] The critical point(s) =…

A: For critical points put f'(x)=0.

Q: If f(x) = > anx", where the coefficients in the ex- n=0 pansion satisfy En(n + 2)anx" + (n –…

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Q: (5) Find the domain of the function f(x,y) = ²-In(r+2) 2-y√100-2² - y²

A: Remember the following domain For xy, y≠0 For x, x≥0 For lnx, x&gt;0 Given function…

Q: Sa cos(r) dr = ,2 %3D 1 sin(r³) +c cos(r³) + c -1 - sin(r*) + c 3 cos(r³) + c 3 1/3

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Q: Q4) Find the turning points and the local maximum and local minimum of the given function x 5 y =…

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Q: Oind Let g(2) = u(2)+iv(2) be ol complete function hiC →C, h(2) = e¯( v(a)+iu(2). Show that if h is…

A: gz=uz+ivz is a complete function and h:ℂ→ℂ by hz=e-ziuz+vz is a entire functionTo prove: g is a…

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Q: (4 points) Find the absolute maximum and absolute minimum of f(r) = 4r + 3r2 – 6x +1 on the interval…

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