List of top Mathematics Questions on Limit and Continuity asked in KCET

If $f(x) = \begin{cases} ax + 7 & \text{if } x<1 \\ 2x - 3 & \text{if } x = 1 \\ \frac{x+b}{b} & \text{if } x>1 \end{cases}$ is continuous at $x = 1$, then

If $\lim_{x \to 3} \left( \frac{x^2 - ax - 3a}{x - 3} \right) = 5$, then $a + b =$

If $f(x) = \begin{cases} x^2 - 1 & \text{if } x \ge 2 \\ x + 1 & \text{if } x<2 \end{cases}$, then $\lim_{x \to 2^+} f(x) + \lim_{x \to 2^-} f(x) = $