Period and Range
The smallest period of a function and an estimate of its range, with a graph and the solution.
f(x) =
x
Examples: 2 sin(3x) + 1, tg(x/2), sin(x)^2, abs(cos x), x/(x^2 + 1). The variable is x.
This calculator finds the smallest positive period of a function, estimates its range E(f) and draws the graph.
Period
The period T is a number such that f(x + T) = f(x) for every x. sin(kx + b) and cos(kx + b) have period 2π/|k|, tg(kx + b) and ctg(kx + b) have period π/|k|. The period of a sum is the least common multiple of the periods of the terms when their ratio is rational.
Example. 2 sin(3x) + 1 has period 2π/3 and its values lie in [−1, 3].
Accuracy
The range is a numerical estimate. It is a handy check, not a replacement for an analytical solution.
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