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.
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just apply the mean value theorem for the function $\displaystyle f(t)=\sin t$ on the interval $\displaystyle [a,b].$
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.
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