If \lim_{x \rightarrow a^{+}} f(x)=p, \lim_{x \rightarrow a^{-}} f(x)=m and f(a)=k, then which one of the following is true? [AP EAPCET 21 May 2025 S2]

Correct Answer is : When p−m=0 and p−k=0, then f(x) is right continuous at x=a

When p-k \neq 0 and m-k \neq 0, then f(x) is continuous at x=a .

When p-k=0 and m-k \neq 0, then f(x) is left continuous at x=a

When {\p}- {\k} \neq 0 and {\m}- {\k}=0, then {\f}( {\x}) is right continuous at {\x}= {\a}

When p-m=0 and p-k=0, then f(x) is right continuous at x=a

Limits Continuity and Differentiability

Section: Mathematics

Question : 15 of 61

Marks: +1, -0

lim

x⟶a+

f(x)=p,

lim

x⟶a−

f(x)=m and f(a)=k, then which one of the following is true?

[AP EAPCET 21 May 2025 S2]

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