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in Limit, continuity and differentiability by (54.8k points)

The value of lim(x π/2) (2-cosx - 1)/x(x - π/2) is

(A) ln2/π

(B) 2ln2/π

(C) 3ln2/π

(D) 4ln2/π

1 Answer

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by (52.5k points)
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Best answer

Answer is (B) 2ln2/π

lim(x π/2) (2-cosx - 1)/x(x - π/2)

π/2 = y

= lim(y0) (2siny - 1)/(y + π/2)y

= lim(y 0) (2siny - 1)/siny . siny/y . 1/(y + π/2)

= 2ln2/π 

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