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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).
37.
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First Course in Differential Equations (Instructor's)
- 18. Which of the following functions has a graph that opens upward? A. f(x) = (x – 7)² – 3 B. f(x) = 7 – (x + 2)² C. f(x) = - (x + 2)2 + 1 D. f(x) = – (x – 2)² – 10 19. Which of the following functions has a graph that opens downward? A. f(x) = (x + 8)² – 5 B. f(x) = (x + 2)² + 9 C. f (x) = 8+ 3 (x + 2)² D. f (x) = 12 – 3 (x + 2)2 %3D 20. What can you say about a parabola that opens downward? A. It has a minimum value B. It has a maximum value C. both and b 21. How would you describe the parabola f (x) = -x? A. Its vertex is at point (0,0) and it opens upward. B. Its vertex is at point (0,0) and it opens to the left. C. Its vertex is at point (0,0) and it opens downward. D. Its vertex is at point (0,0) and it opens to the right. 22. What do you call the graph of a quadratic function? B. Parabola C. Axis of symmetry A. Vertex Youth Army of Masigasig National High School build 2 squares. The Tom more than that of thearrow_forward1 7. Let f(x) = and g(x) 1-x 1 Show that if b + 0, %3D %3D ax +b then g(x) = f (-;x).arrow_forward1 4. Find three functions f, g,h that satisfy: f(g(h(x)))= +2arrow_forward
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- Determine the numbers at which the function is continuous. 1. f(x)= x2(x + 3)² 2. f(x) = (x – 5)³(x² + 4)5 %3| 3. f(x)=-3 х- 2 4. f(x) = x2+2x-8 3x 5. f(x) = if x < 2 1 (4 – x² if 2arrow_forwarddetermine the possible points of discontinuityarrow_forward3. Consider the function f(x) = r - : 1+x 1-x a. Explain why, when evaluated in a floating point system, this expression is subject to a large increase of its relative error (catastrophic cancelation) when x is a very small number. b. Find a formula that is equivalent to the one above in exact mathematics and that does not suffer of catastrophic cancelation.arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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