# SOLUTION: use the bisection method to find each of the zeros of the function: a) f(x)=x^2+x-1 on [-1, 1] b) f(x)= 2x^3-x-3 on [0,2] c) f(x)= sin x-x/2 on [1,3] d) f(x)=2^x-x-1 on [0,2]

Algebra ->  Algebra  -> Trigonometry-basics -> SOLUTION: use the bisection method to find each of the zeros of the function: a) f(x)=x^2+x-1 on [-1, 1] b) f(x)= 2x^3-x-3 on [0,2] c) f(x)= sin x-x/2 on [1,3] d) f(x)=2^x-x-1 on [0,2]      Log On

 Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations! Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help!

 Algebra: Trigonometry Solvers Lessons Answers archive Quiz In Depth

 Click here to see ALL problems on Trigonometry-basics Question 534295: use the bisection method to find each of the zeros of the function: a) f(x)=x^2+x-1 on [-1, 1] b) f(x)= 2x^3-x-3 on [0,2] c) f(x)= sin x-x/2 on [1,3] d) f(x)=2^x-x-1 on [0,2]Answer by Edwin McCravy(8999)   (Show Source): You can put this solution on YOUR website!```I'll just do c) f(x)= sin(x)- on [1,3] Method: 1. Make two columns with headings x and f(x) 2. evaluate f(x) for each of the two first values, they should have different signs. 3. To find the next value of x, average the last two values of x for which the values of f(x) had different signs: 4. Continue until three consecutive values for x when rounded to the desired number of decimal places are the same. You didn't say how accurate, so I will get the zero to the nearest hundredths x f(x) 1 .34147098 3 -1.35888 average 1&3 2 -.0907026 average 1&2 1.5 .24749499 average 2&1.5 1.75 .10898595 average 2&1.75 1.875 .01658578 average 2&1.875 1.9375 -.0783219 average 1.875&1.9375 1.90625 -.0088639 average 1.875&1.90625 1.890625 .0039768 average 1.90625&1.890625 1.8984375 -.0024147 average 1.890625&1.8984375 1.890234375 .00429485 average 1.8984375&1.890234375 1.894335938 .00094806 average 1.8984375&1.894335938 1.896386719 -.0007313 average 1.894335938&1.896386719 1.895361329 .00010887 average 1.896386719&1.895361329 1.895874024 -.0003111 Those last three values of x rounded to the nearest hundredth are both 1.90, so that is the value of the zero of f(x) between 1 and 3. Edwin```