In Problems 7–12 represent the given function by an appropriate cosine or sine
7.
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Differential Equations with Boundary-Value Problems (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_forward.4 Evaluate J2 sec -1 Va drarrow_forwardIn Problems 33–44, determine algebraically whether each function is even, odd, or neither. 34. f(x) = 2x* –x? 38. G(x) = Vĩ 33. f(x) = 4x 37. F(x) = V 35. g(x) = -3x² – 5 39. f(x) = x + |x| 36. h (х) — Зx3 + 5 40. f(x) = V2r²+ 1 x² + 3 -x 42. h(x) =- 1 2x 44. F(x) 41. g(x) 43. h(x) x2 - 1 3x2 - 9arrow_forward
- 7. Find the first 3 iterates of the function f(x) = 3x when xo = 2? O 6, 18, 54 2, 6, 18 O 5, 15, 45 5,6, 54 escarrow_forwardDetermine whether the pairs of functions in Problems 20 through 26 are linearly independent or linearly dependent on the real line. 20. f(x) = 1, g(x) = cos² x + sin? x 21. f(x) = x³, g(x) = x²|x| 22. f(x) = 1+ x, g(x) = 1+ |x| 23. f(x) = xe*, g(x) = |x|e* 24. f(x) = sin? x, g(x) = 1 – cos 2.x 25. f(x) = e* sin x, g(x) = e* cos x 26. f(x) = 2 cos x + 3 sin x, g(x) %3D = 3 cos x – 2 sin xarrow_forward10. Find the first 3 iterates of the function f(x)= 3x when 2n = 2? O 5, 15, 45 O 2, 6, 18 O 5, 6, 54 O 6, 18, 54arrow_forward
- .2 re² -dzdy In (x)arrow_forwardCalculus Questionarrow_forward1. In the figure below, find the number(s) "c" that Rolle's Theorem promises (guarantees). 10 For Problems 2–4, verify that the hypotheses of Rolle's Theorem are satisfied for each of the func- tions on the given intervals, and find the value of the number(s) "c" that Rolle's Theorem promises. 2. (a) f(x) = x² on |-2, 2 (b) f(x) = x² =5x +8 on [0,5] 3. (a) f(x) = sin(x) on [0, 7] (b) f(x) = sin(x) on [A,57]| 4. (a) f(x) = r-x+3 on | 1,1] (b) f(x) = x cos(x) on (0, [0, 1arrow_forward
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