Concept explainers
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.
Want to see the full answer?
Check out a sample textbook solutionChapter 2 Solutions
Differential Equations with Boundary-Value Problems (MindTap Course List)
- In Problems 2–4, for the given functions fand g find: (a) (f° g) (2) (b) (g • f)(-2) (c) (fo f) (4) (d) (g ° 8) (-1) 2. f(x) = 3x – 5; g(x) = 1 – 2r 3. f(x) = Vx + 2: g(x) = 2x² + 1 4. f(x) = e"; g(x) = 3x – 2arrow_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
- In Problems 23–28, answer the questions about the given function. x² + 2 26. f(x) = x + 4 23. f(x) = 2x? - x - 1 (a) Is the point (-1, 2) on the graph of f? (b) If x = -2, what is f(x)? What point is on the graph of f? (c) If f(x) = -1, what is x? What point(s) are on the graph of f? (d) What is the domain of f? (e) List the x-intercepts, if any, of the graph of f. (f) List the y-intercept, if there is one, of the graph of f. 24. f(x) = -3x² + 5x (a) Is the point (-1, 2) on the graph of f? (b) If x = -2, what is f(x)? What point is on the graph of f? (c) If f(x) = -2, what is x? What point(s) are on the graph of f? (d) What is the domain of f? (e) List the x-intercepts, if any, of the graph of f. (f) List the y-intercept, if there is one, of the graph of f. x + 2 (a) Is the point ( 1,) on the graph of f? (b) If x = 0, what is f(x)? What point is on the graph of f? (c) If f(x) =5. what is x? What point(s) are on the graph of f? (d) What is the domain of f? (e) List the x-intercepts, if…arrow_forwardIn Problems 29–40: (a) Find the domain of each function. (d) Based on the graph, find the range. (b) Locate any intercepts. (e) Is f continuous on its domain? S3x 14 (c) Graph each function. S2r 29. f(x) : if x + 0 S-2x + 3 3x – 2 if x 1 x + 3 2x + 5 if -3 sx0 S1 + x if x 0 35. f(x) : 36. f(x) = 37. f(x) if x 20 S2 - x if -3 sx1arrow_forward23. What is the domain of the function f(x) = Vx² – 16? %3D In Problems 25–32, use the given functions f and g. (a) Solve f(x) = 0. (e) Solve g(x) s 0. (b) Solve g(x) = 0. (f) Solve f(x) >g(x).arrow_forward
- 4. Suppose the following functions are a general solution of: y(4) + a3y" +a2y" + a1y' + a0y = 0arrow_forwardPage 3 Question 4 (a) Find the following: x1/3 + 9x/5 (2х — 1)4/2 — 3 i. Lim- x0 6x1/2 – 4x1/4 ii. Lim X→5+ (b) The total revenue curve of a firm is R(q) = 40q – 12q2 and its q² – 12.85q + 20 + 30 400 -, where q is the firm's output. average cost A(q) Derive an expression C(q) for the firm's total cost function. ii. Derive an expression II(q) for the firm's profit function. iii. Is the rate of change of profit increasing or decreasing when the ouput level of the firm is 10 units? iv. Determine the level of output for which the firm's profit is maximized. v. What is the firms's maximum profit? i.arrow_forward14. Find the value of the constants (a, b, or c) that makes the following functions continuous: -1 if x 1/1/2 (a) f(0) = x²_c if x < 5 4x + 2c if x 5 (b) f(x)= =arrow_forward
- 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. If f(x) is a function such that f(1) = 2, f(n + 1) = (3f(n)+1)/3 for n = 1, 2, 3, ..., what is the value of f(100)?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_forward
- Discrete Mathematics and Its Applications ( 8th I...MathISBN:9781259676512Author:Kenneth H RosenPublisher:McGraw-Hill EducationMathematics for Elementary Teachers with Activiti...MathISBN:9780134392790Author:Beckmann, SybillaPublisher:PEARSON
- Thinking Mathematically (7th Edition)MathISBN:9780134683713Author:Robert F. BlitzerPublisher:PEARSONDiscrete Mathematics With ApplicationsMathISBN:9781337694193Author:EPP, Susanna S.Publisher:Cengage Learning,Pathways To Math Literacy (looseleaf)MathISBN:9781259985607Author:David Sobecki Professor, Brian A. MercerPublisher:McGraw-Hill Education