Functions Question 398
Question: If $ f(x)= \begin{cases} \frac{x^{2}-9}{x-3},, & \text{if }x\ne 3 \\ 2x+k,, & otherwise \\ \end{cases} . $ , is continuous at $ x=3, $ then $ k= $
[Kerala (Engg.) 2002]
Options:
A) 3
B) 0
C) ?6
D) 1/6
Show Answer
Answer:
Correct Answer: B
Solution:
$ \underset{x\to 3}{\mathop{\lim }},f(x)=\underset{x\to 3}{\mathop{\lim }},\frac{x^{2}-9}{x-3}=\underset{x\to 3}{\mathop{\lim }},(x+3)=6 $ and $ f(3)=2(3)+k=6+k $ $ \because f $ is continuous at $ x=3 $ ; \ $ 6+k=6\Rightarrow k=0 $ .
BETA
