Question
Examine the following functions for continuity.
f(x) = x - 5
f(x) = x - 5
Function f is defined for all real numbers.
Let c be any real number.
$\therefore$ f(c) = c - 5
Also $\ \ \ \text{Lt}\ \ \ \ \ \text{f(x)}\\ \text{x}\rightarrow{\text c}$ = $\ \ \ \text{Lt}\ \ \ \ \ \ \ (\text x - 5) = \text{c} - 5\\ \text{x}\rightarrow{\text c}$
$\therefore \text{Lt}\ \ \ \ \ \text{f(x)} = \text{f(c})\\ \ \ \text{x}\rightarrow{\text c}$
$\therefore$ f is continuous at x = c
But c is any real number.
$\therefore$ f is continuous at every real number.
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
| $\text{X}$ | $0$ | $1$ | $2$ | $3$ |
| $\text{P}(\text{X})$ | $\text{k}$ | $\frac{\text{k}}{2}$ | $\frac{\text{k}}{4}$ | $\frac{\text{k}}{8}$ |
Find $\text{P}(\text{X}\leq2)+\text{P}(\text{X}>2)$