A) 7
B) ?7
C) \[\pm 7\]
D) None of these
Correct Answer: A
Solution :
For continuous \[\underset{x\to 2}{\mathop{\lim }}\,\,f(x)=f(2)=k\] \[\Rightarrow \,\,k=\underset{x\to 2}{\mathop{\lim }}\,\frac{{{x}^{3}}+{{x}^{2}}-16x+20}{{{(x-2)}^{2}}}\] \[=\underset{x\to 2}{\mathop{\lim }}\,\,\frac{({{x}^{2}}-4x+4)\,\,(x+5)}{{{(x-2)}^{2}}}=7\] .
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