Assertion (A) If a function f is discontinuous at c, then c is called a point of discontinuity. Reason (R) A function is continuous at x=c, if the function is defined at x=c and the value of the function at x=c equals the limit of the function at x=c.

Question

Assertion (A) If a function f is discontinuous at c, then c is called a point of discontinuity. Reason (R) A function is continuous at x=c, if the function is defined at x=c and the value of the function at x=c equals the limit of the function at x=c. (A) Both A and R are correct; R is the correct explanation of A (B) Both A and R are correct; R is not the correct explanation of A (C) A is correct; R is incorrect (D) R is correct; A is incorrect

Tardigrade Admin · Accepted Answer

A function is continuous at x=c, if the function is defined at x=c and if the value of the function at x=c equals the limit of the function at x=c. And if f is not continuous at c, we say f is discontinuous at c and c is called a point of discontinuity of f.

Q. Assertion (A) If a function $f$ is discontinuous at $c$ , then $c$ is called a point of discontinuity.
Reason (R) A function is continuous at $x = c$ , if the function is defined at $x = c$ and the value of the function at $x = c$ equals the limit of the function at $x = c$ .

Both A and R are correct; R is the correct explanation of A

Both A and R are correct; R is not the correct explanation of A

A is correct; R is incorrect

R is correct; A is incorrect

A function is continuous at $x = c$ , if the function is defined at $x = c$ and if the value of the function at $x = c$ equals the limit of the function at $x = c$ . And if $f$ is not continuous at $c$ , we say $f$ is discontinuous at $c$ and $c$ is called a point of discontinuity of $f$ .

Q. Assertion (A) If a function f is discontinuous at c, then c is called a point of discontinuity. Reason (R) A function is continuous at x=c, if the function is defined at x=c and the value of the function at x=c equals the limit of the function at x=c.