# 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 a n approximate root of f(x) within 1/8 accuracy.

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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 a n approximate root of f(x) within 1/8 accuracy.

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Step 1

According to Intermediate Value theorem,

Any continuous function f has a solution in the interval [a,b] such that f(c)=L where c is the root in the interval (a,b) and L is the any value lying between f(a) and f(b).

Step 2

Calculate f(1) and f(2).

Step 3

Apply intermediate theorem,

function f(x) is a continuous function on the closed interval [1,2] , f(1)=-6 and f(2)=10. Since -6<L<10 there is a number c in (1,2) such that f(c)=L by t...

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