Question

If f(x) is continuous at x = a and$\underset{x\to a^{-}}{\lim }f\left(x\right)=\underset{x\to a^{+}}{\lim }f\left(x\right)=k,$ then k is equal to _____________.

Answer 1

It is given that, f(x) is continuous at x = a.

$\therefore f\left(a\right)=\underset{x\to a^{-}}{\lim }f\left(x\right)=\underset{x\to a^{+}}{\lim }f\left(x\right)$ .....(1)

Also,

$\underset{x\to a^{-}}{\lim }f\left(x\right)=\underset{x\to a^{+}}{\lim }f\left(x\right)=k$ .....(2)

From (1) and (2), we have

f(a) = k

Thus, the value of k is f(a).


If f(x) is continuous at x = a and$\underset{x\to a^{-}}{\lim }f\left(x\right)=\underset{x\to a^{+}}{\lim }f\left(x\right)=k,$ then k is equal to $\underline{f\left(a\right)}$.