As x approaches (π)/(2), the quotient (1-sin x)/((fracπ2-x)^2 approaches the value
Single correct option
As x approaches 2π, the quotient (2π−x)21−sinx approaches the value
A.1
B.0
C.21
D.2
Show answer and solution
Answer:(C) 21
Put h=2π−x→0, so sinx=cosh and the expression becomes h21−cosh→21. Trap: differentiating once (L'Hopital) gives −2(2π−x)−cosx→00 again, and stopping there or assuming the limit is 0 or 1 is common; the standard result h21−cosh→21 settles it.