Read the two statements and choose the correct option.
I. A function can have a limit at $x = a$ without being continuous there.
II. If $f$ is continuous at $x = a$ , then $\lim_{x \to a} f(x) = f(a)$ .

Only ICorrect answerYour answerOnly IICorrect answerYour answerBoth I and IICorrect answerYour answerNeither I nor IICorrect answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer C

Correct answer: C

I: $f(x) = x^{2}$ for $x \ne 2$ with $f(2) = 5$ has limit 4 at 2 but is not continuous. True.
II is the definition of continuity at $a$ . True.

Ten questions from Continuity & Differentiability, at your own pace.

Ten questions from Continuity & Differentiability, at your own pace.

Read the two statements and choose the correct option.I. A function can have a limit at x=ax = ax=a without being continuous there.II. If fff is continuous at x=ax = ax=a, then lim⁡x→af(x)=f(a)\lim_{x \to a} f(x) = f(a)limx→a​f(x)=f(a).