Question

$\lim _ { x \rightarrow 1 }$ $\sin\left| ||x| - 2| - 3 \right|$ is-

• A. sin 2
• B. sin 1
• C. 0
• D. Does not exist

Answer 1

Answer: (A)

sin 2

Answer 2

R.H.L. $\lim_{h \rightarrow 0}$sin ||1 + h –2| –3|

$\lim_{h \rightarrow 0}$sin | 1 – h –3| Ž $\lim_{h \rightarrow 0}$sin (2 + h) = sin 2

L.H.L.

$\lim_{h \rightarrow 0}$sin |1 (1 – h) –2| –3|

$\lim_{h \rightarrow 0}$sin |1 + h –3| Ž $\lim_{h \rightarrow 0}$ sin (2 – h) = sin 2