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- Use (a) bisection method and (b) false position method to find the solution to the following within error of 10-6. Show your manual solution for first three iterations, then prepare an Excel file for the finding the root until the error is within 10-6 showing also the graph of the function. x3-2x2-5=0, when x = [1, 4] sin x - e-x=0, when x = [0,1] (x-2)2-ln x =0, when x = [1,2]5. Carry out the first three iterations by using bisection method to find the root of e^x−3x =0 on (0, 1).1. Use the Intermediate Value Theorem to nd an interval of length one that contains a root of f(x) = sin2(x) - x - ex. Then write the iterations of Bisection method to an approximate root of f(x) within 1/8 accuracy.
- Why is it that lim of ln|t-1/t+2| = ln|1|? This then yields us 0. But how did we get 1 from infinity over infinity?find lim x->0 cos(12x) -1/3x. not using the l'hospital rule. must show all stepsProve that sinh x is an odd function of x and that cosh x is an even function of x, and check that this is consistent with the graphs in Figure 6.9.1.
- Find an approximate solution of the first root of the following function using the secant method. Consider the interval [0,1-0,5] with an allowable error of 10^-2Use the secant method to approximate one of the real roots of f(x) and complete Table III. Use initial values at x−1=1 and x0=1.3. Perform as many iterations as necessary until ea<5%.I now know about the even function rule where you can change the bounds from -a to a to 0 to a by putting a 2 out front of the integral for any "even function." After asking my first question about that the new solution did not use that method and instead used -2 to 2 as in the original problem, this makes the answer 0 and if you use the even function method and pull the 2 out front the answer is pi/2. Which of these is the correct answer? How do we know when we can use that even function rule or when not to. I noticed the rule said an even function is when f(-x)=f(x) but I'm not exactly sure what that means
- 7. Use a graph of f(x)= 3+(sin(x^2)/x^2) to estimate the smallest number N so that |(3+(sin(x^2)/x^2))-3|<0.00001 whenever x>N. Make sure and illustrate, on the graph, how you found your value for N. This question is from limits so maybe you somehow have to use the defitnition of limits to solve it because |f(x)-L|<epsilon is given.Find Lim as x approaches 0 of the function cos(4x-1)/2xUse (a) bisection method and (b) false position method to find the solution to the following within error of 10-6. Show your manual solution for first three iterations, then prepare an Excel file for the finding the root until the error is within 10-6 showing also the graph of the function. 1.sin x - e-x=0, when x = [0,1]