Question

-0.2r 2.5x using the bisection method (1 point) In this problem you will approximate a solution of e Instead of solving e22.5x, you can let f(z) 027 - 2.5z and solve f(z) 0 First find a rough guess for where a solution might be Evaluate f(x) at -4,-3,-2,-1,0, 1,2,3, and 4. Remember that you can make Webwork do your calculations for you! f(-4) f(-3) f(-2) f(0)- f(1) = f(2) - f(3) - f(4) Using your answers above, the Intermediate Value theorem guarantees that there is a solution to f(x) z-values make f(a) positive, and which make f(z) negative 0 with z in what interval? Think about which of the above There is guaranteed to be a solution in (Enter your answer in interval notation.) Take your interval from part (b) and cut it in half. What r-value is right in the middle? Halfway point is Evaluate f(x) at this halfway point: At the midpoint of the interval from part (b), f(z) - Using your answers above, what is the smallest interval in which the intermediate value theorem guarantees that there will be a solution to f(x) = 0? At the midpoint of the interval from part (b), f(a) Using your answers above, what is the smallest interval in which the intermediate value theorem guarantees that there will be a solution to f(z) = 0? There is guaranteed to be a solution in Hint: One endpoint of your interval should be the halfway point you just found (Enter your answer in interval notation.) Now repeat step (c) as follows. Take your interval from part (c) and cut it in half. What x-value is right in the middle? Halfway point is Evaluate f(z) at this halfway point: At the midpoint of the interval from part (c), fx) Using your answers above, what is the smallest interval in which the Intermediate Value theorem guarantees that there will be a solution to f(x) = 0? There is guaranteed to be a solution in Hint: One endpoint of your interval should be the haltway point you just found (Enter your answer in interval notation.) Repeat part (d) again. Now what is the smallest interval in which the Intermediate Value theorem guarantees that there will be a solution to f(x) = 0? There is guaranteed to be a solution in (Enter your answer in interval notation.) Repeat part (e) one last time. Now what is the smallest interval in which the Intermediate Value theorem guarantees that there will be a solution to f(x) = 0? There is guaranteed to be a solution in (Enter your answer in interval notation.) You started with your interval in part (b), then cut it in half 4 times. What is the length of the interval you ended up with? Interval has length If you were to repeat the bisection step 6 more times, what length interval would you end up with? Interval would have length

Answer 1

1-3〉二)9.sv.n_ -) (-*) = 16.49, 8 fc-68126 The root e

let- les-