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Question: \(\lim_{x \rightarrow 2^{+}}\) {x} \(\frac{\sin(x–2)}{(x–2)^{2}}\) =...

lim⁡x→2+\lim_{x \rightarrow 2^{+}} {x} sin⁡(x–2)(x–2)2\frac{\sin(x–2)}{(x–2)^{2}} =

A

0

B

C

1

D

Does not exist

Answer

1

Explanation

Solution

x ® 2+ Ž x = 2 + h

limit = lim⁡h→0\lim_{h \rightarrow 0}{2 + h} sin⁡(2+h–2)(2+h–2)2\frac{\sin(2 + h–2)}{(2 + h–2)^{2}}

= lim⁡h→0\lim_{h \rightarrow 0} h × sin⁡hh2\frac{\sin h}{h^{2}} = 1.