Question

Show that the equation has exactly one real root.
2x-100-sinx=0

Answer 1

Let f(x) = 2x - 1 - sin(x)

Notice that,

f(0) < 0 and f(2) > 0

Therefore, by the Intermediate Value theorem there exists a zero in the interval [0, 2].

Now, is this the only root?

f'(x) = 2 - cos(x) > 0 for all x. Therefore, f(x) is strictly increasing and therefore, the root we found above is the ONLY root.

Hope this helps!

Answer 2

Thanks Harry!

Answer 3

Welcome! :D