Functions Question 116
Question: If $ f(x)= \begin{cases} & x+\lambda ,\ x,<3 \\ & ,4,x=3 \\ & 3x-5,x>3 \\ \end{cases} . $ is continuous at $ x=3 $ , then $ \lambda = $
[MP PET 1994, 2001; RPET 1999]
Options:
A) 4
B) 3
C) 2
D) 1
Show Answer
Answer:
Correct Answer: D
Solution:
By definition of continuity, we know that $ \underset{x\to 3+}{\mathop{\lim }},f(x)=f(3)=\underset{x\to 3-}{\mathop{\lim }},f(x) $
$ \Rightarrow ,\underset{x\to 3-}{\mathop{\lim }},f(x)=4 $ or $ \underset{h\to 0}{\mathop{\lim }},3-h+\lambda =4 $ $ f(3)=3.7 $
BETA
