Question

$li{m}_{x\to 0}$ $\frac{\left(x^{3}cotx\right)}{1-cosx}$ =


[AI CBSE ; DSSE 1988]

• A. 0
• B. 1
• C. 2
• D. -2

Answer 1

The correct option is C

2

$li{m}_{x\to 0}$ $\frac{\left(x^{3}cotx\right)}{1-cosx}$
= $li{m}_{x\to 0}$ ($\frac{x^{3}cotx}{1-cosx}$ × $\frac{1+cosx}{1+cosx}$)
= $li{m}_{x\to 0}$ ${\left(\frac{x}{sinx}\right)}^3$ × $li{m}_{x\to 0}$ cosx × $li{m}_{x\to 0}$ (1+cos x) =2