Answer to Question #180117 in Linear Algebra for Oliver

Question #180117

Solve the following question by using bisection method.

upto six iteration


X³ - X - 11 = 0


1
Expert's answer
2021-04-15T07:33:14-0400

Set

f(x)=x3x11f(x) = x^3 -x-11

Consider when x = 2, then f(2) = -5 < 0

Also, consider when x = 2.5, then f(2.5) = 2.125>0

Since we have that f(2).f(2.5) < 0. We can state that the solution lies in the interval [2,2.5]


Iteration 1:

m=2+2.52=2.25m = \dfrac{2+2.5}{2} = 2.25

f(2.25) = -1.8594 < 0

So we replace 2 with 2.25


Iteration 2:

m=2.25+2.52=2.375m = \dfrac{2.25+2.5}{2} = 2.375

f(2.375) = 0.0215>0

So we replace 2.5 with 2.375


Iteration 3:

m=2.25+2.3752=2.3125m = \dfrac{2.25+2.375}{2} = 2.3125

f(2.3125) = -0.946 < 0

So, we replace 2.25 with 2.3125


Iteration 4:

m=2.3125+2.3752=2.3438m = \dfrac{2.3125+2.375}{2} = 2.3438

f(2.3438) = -0.4684 < 0

So, we replace 2.3125 with 2.3438


Iteration 5:

m=2.3438+2.3752=2.3594m = \dfrac{2.3438+2.375}{2} = 2.3594

f(2.3594) = -0.2251 <0

So, we replace 2.3438 with 2.3594


Iteration 6:

m=2.3594+2.3752=2.3672m = \dfrac{2.3594+2.375}{2} = 2.3672

f(2.3672) = -0.1023<0


So the solution of x3x11=0x^3 -x-11 = 0 is 2.3672 in the interval [2,2.5], using bisection method up to 6 iterations.


Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!

Leave a comment