Σ Suppose that ax" converges to a function y such that y" – 2y' + y = 0 where y(0) = 0 and y'(0) = 1. Find a formula that relates a, + 2, a, + 1, and a, n = 0 Compute a, ag. , - 1 1 a, = 1 az = 2! 1 a4 = 3! 1 as = 4!

Q: Chapter 4, Section 4.3, Question 024 Given the functionf (x) = x³ + 3x² – 45x + 8 over the interval…

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Q: Show that, for any constant k, f(x)' dxL k f'(x) k

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A: Integrating on both sides, we get

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Q: lim (x' – 2x* +5)= x→-2 O a. 22 O b. -11 O C. -13 O d. -18

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Q: Let 7(t) = Find 7'(t) 7 (t) =

A: Topic - vectors and derivatives Since r→t = 5 t5-1, -e-t, -3 sin2t we to find r→'t  derivative of tn…

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Q: f"(x) = 20x3 + 12x2 + 4 with the initial conditions f(0) particular f(x). = 8 and f(1) = 5. Det

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Q: pose f'(x) = √(x+3) and f(1) = 0. Find a formula for f(x) and show all of your work.

A: Given query is to find the function.

Q: 6. Find [ f(x)dx if f(x) = et -1, if -3<x<0 V9-x², if 0<x<3

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Q: Suppose f'(x) = c for all x, where c is a constant. Show that, for some constant d, f(x) = cx + d.

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Q: The graph of f is shown in the figure. 6. 4 х 14 -4 -6+ 2-

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Q: 03: Let S(x)=12-x-1|-1. -1. Find f"(0) and Find f'(4)

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Q: The force of interest, X, at time ,t, is given by X(t) = 0.02 for 0 < t< 5 and X(t) = 0.05 for t ≥ 5…

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