Problem 4. Sketch the graph of the given function, and then re-express it in terms of a sum of step functions w(t).Confirm your graph looks correct using the Desmos template above. (this is §6.3 # 5, 7)(b) f(t)=Le-t-2,0

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Answered: Problem 4. Sketch the graph of the…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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1. Graph f(x) ● ● L ● = x³-7x² +17x-15 = x-3 2. Using the function f (x) from #1. Use your calculator to determine the two numbers close to 3 between which x must be kept if f(x) is to stay within 0.01 units of Give a short explanation of how you calculated these values, 2 For the statement "If x is within ___ units of 3 (but not equal to 3), then f(x) is within 0.01 of 2", state the largest number that can go in the blank The formal definition of a limit is: x →C lim f(x)if and only if for any positive number € (no matter how small) there is a positive number & such that if x is within & units of c, f(x) is within € units of L. The four numbers L, c, e, and 8 all appear in the problem above. Which one is which? Explain on your graphing calculator: Find f(3) Explain what this means Find lim f(x) x 3 Explain how you determined the limit
11. The graphs off and g are given. Express the function g in the form g(x) = a (x-h)² + k f(x)=x² ◄▬▬▬▬▬▬▬▬▬ -7 -5 -3 17 14+ 10 6 2 + 1 + 1 3 9 + + 5 7 Copyright Cengage Learning. Powered by Cognero. + + + 9 11 13 Page 3
For #1-9, suppose a ball's heights in feet at time t in seconds is given by s(t) = 64 - 16(t-1)² 1. Sketch a graph of y = s(t) on the time interval [0, 3]. Label the points on the graph that correspond to when the ball is released, when it reaches its highest point, and when it lands. 2. How does the ball's motion differ on the time intervals (0, 1) and (1, 3)? What occurs at the instant t = 1? 3. Compute the ball's average velocity on the following time intervals. Include units for each. (a) [0.4, 0.8] (e) [0.8, 1.2] (b) [0.7,0.8] (c) [0.79, 0.8] (d) [0.799, 0.8] (f) [0.8,0.9] (g) [0.8, 0.81] (h) [0.8, 0.801]
The boxes outlined in green are correct, but I can't figure out what the red ones are.
If we shift the graph of f(x) = 3/x by one unit upward and two units to the left then we get the graph of the function: O g(x) = 3vx +2+1 Og(x) = 3\x – 2 – 1 O g(x) = 3vx +2 – 1 O g(x) = 3Vx – 2+1 None of the above
3. Given h (t) = -3t + 12t, find and simplify h(a)-h(1) a-1 4. Use the graph of this function to determine what intervals it is increasing, decreasing, or constant on
4. Sketch the graph of the function. x-1)² +2(x-1)+6 a. 1 x+1 if xe(-0,1] if xe (1,3) if x e[3,5] -x+1 b. g(x) =. x+1 if x e(5, 0)
7. 2. Function below is hanskated 3 units right, Then reflected across the y-cods to create functiong. Which equation represents g? O A B U D A. g(x)=√(x-1) B. g(x)=√(x+1) C. g(x)=-1 D. (x)--√√x+1 E: All of the Above
1. Describe how the graph of the function can be obtained from one of the basic graphs: 1 y = x y = 22 y = VI y = r3 y = VI y y = |r| (a) f(x) = (x+ 3)² (b) f(r) = x2 +3 (c) f(x) = 12 - %3D (d) h(x) = -VI (e) h(x) = V- 1 (f) g(x) = 1 (g) g(x) = (h) g(x) = |x+2| – 3 (i) f(x) = VI + 2 (6) f(x) =D -글V-1 (k) f(r) = 2VT– 4 (1) f(r) = 2V - 4 4 (m) f(r) = . 2 (n) f(x) = 5 - (0) f(x) %3D 옮교3-4 (p) g(x) = -(x – 3)2 + 5 4.

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Problem 4. Sketch the graph of the given function, and then re-express it in terms of a sum of step functions w(t). Confirm your graph looks correct using the Desmos template above. (this is §6.3 # 5, 7) (b) f(t)= Le-t-2, 0