Calculus/Calculus

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Expert: - 9/22/2008


Question
I have to Use Intermediate value theorem to prove
sinx-x/2 =0 has a solution in the interval [1,2]

Answer
According to //en.wikipedia.org/wiki/Intermediate_value_theorem , one way to express the intermediate value theorem is

 The intermediate value theorem states the following: If the
 function y = f(x) is continuous on the interval [a, b], and u is a
 number between f(a) and f(b), then there is a c ∈ [a, b] such that
 f(c) = u.

Here, we have a=1, b=2, and f(x) = sin(x) - x/2.
It can be seen that f(a)=f(1)= 0.341470985 and that
f(b) = f(2) = -0.090702573.

Since 0 is between -0.0907... and .34147..., there must be some value c in (1,2) such that f(c) = 0 since 0 is between the two values given.

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