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Evaluate : [underset(x to 0)lim (tan x)/...

Evaluate : `[underset(x to 0)lim (tan x)/(x)]`, where `[*]` represents the greatest integer function.

Text Solution

Verified by Experts

See the graph of y=x and `tan^(-1)x` in the figure:

From the figure, when `xto0^(+)`, graph of y=x is above the graph
So,`" "tan^(-1)xltx" or "(tan^(-1)x)/(x)lt1`
`implies" "underset(xto0^(+))lim(tan^(-1)x)/(x)=1^(-)`
`implies" "[underset(xto0^(+))lim(tanx)/(x)]=0`
Thus`" "[underset(xto0)lim(tan^(-1)x)/(x)]=0`
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