I need help please with the following question. (Do I need to use radians in dealing with the sin pa

Gybrisysmemiau7

Gybrisysmemiau7

Answered question

2022-06-14

I need help please with the following question. (Do I need to use radians in dealing with the sin part?))
(a) Use the Intermediate Value Theorem to show that the equation x + sin ( x ) = 1, has at least one solution in the interval [0,1].
(b) Find an approximation of the solution with an error of at most 0.05.

Answer & Explanation

Jake Mcpherson

Jake Mcpherson

Beginner2022-06-15Added 23 answers

(a)Take f ( x ) = x + sin x 1 .Now you can see that f(0) is negative and f(1) is positive, So f(x) will be zero for some intermediate value. So, equation will have a solution.
(b)find f(0.5) and see if it is positive then solution will lie between 0 and 0.5 else it will lie between 0.5 and 1, then go to appropriate range and keep doing it further .

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