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If f(x) + f(y) = f(xy-sqrt(1-x^(2))sqrt(...

If `f(x) + f(y) = f(xy-sqrt(1-x^(2))sqrt(1-y^(2))), f(0) = (pi)/(2)` and f is differentiable in (-1, 1).
Then `|lim_(x rarr 0)(2f(x)-pi)/(x)|=`

Text Solution

Verified by Experts

The correct Answer is:
2
Here `f(x) = cos^(-1)x`
Now `lim_(x rarr 0)(2cos^(-1) x-pi)/(x) ((0)/(0))` form LH Rule
`rArr lim_(r rarr 0)(-2)/(sqrt(1-x^(2))) = -2 rArr |lim_(x rarr 0)(2f(x)-pi)/(x)|= +2`
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