First slide

Introduction to limits

Question

$The value of \lim_{x \to 0^{+}} \frac{\cos^{- 1} (x - [x]^{2}) \cdot \sin^{- 1} (x - [x]^{2})}{x - x^{3}}, where [x] denotes the greatest intege$ $\leq x is$

Moderate

A

0
B

$\frac{π}{4}$
C

$π$
D

$\frac{π}{2}$

Solution

$\lim_{x \to 0^{+}} \frac{\cos^{- 1} x \cdot \sin^{- 1} x}{x (1 - x)} = \frac{π}{2}$

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