Thread: inequalities

Use the inequality absolute value[sin(a)-sin(b)] << absolute value[a-b], which is valid for all real numbers a and b, to prove that sin x is continuous on R.

just apply the mean value theorem for the function on the interval

Is the mean value theorem the same thing as the intermediate value theorem?

IVT
f(x) is defined on [a,b]
f(x) assumes all values of (a,b)
then f(c) where c is a point in (a,b) intersects f(x)

no, the assumptions are different, google it and see.