Functions Question 83
Question: Let $ f(x)= \begin{cases} & \frac{x^{3}+x^{2}-16x+20}{{{(x-2)}^{2}}},if\ x\ne 2 \\ & \ \ \ \ \ ,\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ,\ k,\ if\ x=2 \\ \end{cases} . $ . If $ f(x) $ be continuous for all x, then k =
[IIT 1981]
Options:
A) 7
B) ?7
C) $ \pm 7 $
D) None of these
Show Answer
Answer:
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 $ .
BETA
