We will use this to find the crossing points of two graphs. Consider the two functions...
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We will use this to find the crossing points of two graphs. Consider the two functions f(x) = x5-x-2x +1 and g(x)=x-2 on the interval [-1, 2]. A quick look in GeoGebra shows that the two graphs cross each other three times in this interval: f(x) = x5-x-2x +1 g(x)=x-2 9 -2 3 2 3 Our goal is to use list comprehension to find, by trial and error, approximately for which values of the two graphs cross, i.e.. f(x) = g(x). Do this by considering N equally distributed points on the interval [-1, 3], at each point checking whether f(x) - g(x) < & where is some small (positive) number. More precisely, you should do the following steps: Define f and g using the lambda construction. Let N and & be user input to the program. . Using range and list comprehension create a list [0, 1,..., N-1] of N equally spaced x-values starting at -1 and ending at 2. Use this list of x-values to create a second list [(0.30), (1, 1),... (N-1. UN-1)] of (x, y) tuples; the x-values should just be the x-values from the previous list, while the y value is the difference f(x) - g(x). i.e.. y = f(xi) - g(xi)|. . Then use list comprehension to find those a values of those (x, y) tuples for which y is less than e, and print the list of these values. Run your program with N= 400 and e=0.01. Explain the output from the program. Finally try also other values of N, keeping the value of a fixed. Explain your observation. Can you obtain the approximate a coordinates of all three crossing points? Use a markdown cell after your code to add your observations. We will use this to find the crossing points of two graphs. Consider the two functions f(x) = x5-x-2x +1 and g(x)=x-2 on the interval [-1, 2]. A quick look in GeoGebra shows that the two graphs cross each other three times in this interval: f(x) = x5-x-2x +1 g(x)=x-2 9 -2 3 2 3 Our goal is to use list comprehension to find, by trial and error, approximately for which values of the two graphs cross, i.e.. f(x) = g(x). Do this by considering N equally distributed points on the interval [-1, 3], at each point checking whether f(x) - g(x) < & where is some small (positive) number. More precisely, you should do the following steps: Define f and g using the lambda construction. Let N and & be user input to the program. . Using range and list comprehension create a list [0, 1,..., N-1] of N equally spaced x-values starting at -1 and ending at 2. Use this list of x-values to create a second list [(0.30), (1, 1),... (N-1. UN-1)] of (x, y) tuples; the x-values should just be the x-values from the previous list, while the y value is the difference f(x) - g(x). i.e.. y = f(xi) - g(xi)|. . Then use list comprehension to find those a values of those (x, y) tuples for which y is less than e, and print the list of these values. Run your program with N= 400 and e=0.01. Explain the output from the program. Finally try also other values of N, keeping the value of a fixed. Explain your observation. Can you obtain the approximate a coordinates of all three crossing points? Use a markdown cell after your code to add your observations.
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The graph you sent shows the function fx x2 x3 x4 x5 x6 x7 x8 x9 x10 It is a polynomial function of ... View the full answer
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