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In Problems 37‒40 proceed as in Example 6 to solve the given initial-value problem. Use a graphing utility to graph the continuous function y(x).
40.
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A First Course in Differential Equations with Modeling Applications (MindTap Course List)
- In Problems 11–20, for the given functions f and g. find: (a) (f° g)(4) (b) (g•f)(2) (c) (fof)(1) (d) (g ° g)(0) \ 11. f(x) = 2x; g(x) = 3x² + 1 12. f(x) = 3x + 2; g(x) = 2x² – 1 1 13. f(x) = 4x² – 3; g(x) = 3 14. f(x) = 2x²; g(x) = 1 – 3x² 15. f(x) = Vx; 8(x) = 2x 16. f(x) = Vx + 1; g(x) = 3x %3D 1. 17. f(x) = |x|; g(x) = 18. f(x) = |x – 2|: g(x) x² + 2 2 x + 1 x² + 1 19. f(x) = 3 8(x) = Vĩ 20. f(x) = x³/2; g(x) = X + 1'arrow_forwardIn Problems 13–24, use the graph of the function f given.arrow_forwardIn Problems 19–30, graph the function f by starting with the graph of y = x² and using transformations (shifting, compressing, stretching, and/or reflection). Verify your results using a graphing utility. [Hint: If necessary, write f in the form f(x) = a(x – h)² + k.] 19. f(x) = 20. f(x) = 2x2 + 4 21. f(x) = (x + 2)² – 2 22. f(x) = (x – 3)² – 10 23. f(x) = x² + 4x + 2 24. f(х) — х? — бх — 1 25. f(x) = 2x? – 4x + 1 26. f(x) = 3x? + 6x 4 27. f(x) = -x² - 2x 28. f(x) 3D-2х? + 6х + 2 29, f(x) : 30. f(x) 1 + xarrow_forward
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- 13) Match the graph with the correct function. (b) S) = -1 2r + 1 (a) S(1) %3D %3D 2r +1 ? + 2r + 2 2r - 1 (e) None of these x' + 2r? + x- 2 2x +1 (c) S(x) = (d) S(x) 14)arrow_forward1. Let g(x)= f(t) dt where f is the function whose graph is shown in the figure. -6- -5- -4 -3- -2- -1 + -1 -2- a. Estimate g(0), g(2), g(4), g(6), and g(8).arrow_forwardExpress the solution of the given IVP in terms of a convolution where g(t) is an arbitrary function.arrow_forward
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