Question

If a function f(x) is defined in x $ϵ$ [a, b], then f(x) is continuous at a if

• A. ${lim}_{x\to a}-f\left(x\right)={lim}_{x\to a^{+}}f\left(x\right)=f\left(a\right)$
• B. ${lim}_{x\to a^{+}}f\left(x\right)=f\left(a\right)$
• C. Function will be continuous in any case
• D. Function will be discontinuous in any case

Answer 1

The correct option is B

${lim}_{x\to a^{+}}f\left(x\right)=f\left(a\right)$

For a function f(x) defined in [a, b]. the condition for continuity is that the RHL at a should be = f(a), since there are no value for f(x) for x$<$ a. for the same reason we cant take the left hand limit of the function at x = a.