If \( f(x)=\begin{cases}\lambda x+5 & ,if\quad x\le 2\\x+3 & ,if\quad x\gt 2\end{cases} \) is continuous at \( x=2 \), then, the value of \( \lambda \) is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 0
f is continuous at x = 2 when the left-hand limit, the right-hand limit and f(2) are all equal:
\( \displaystyle f(2)=\lim_{x\to 2^-}(\lambda x+5)=2\lambda+5 \)
\( \displaystyle \lim_{x\to 2^+}(x+3)=5 \)
\( \displaystyle 2\lambda+5=5 \)
\( \displaystyle \lambda=0 \)