Question

If $\lbrack y\rbrack$ is continuous at x = 0, then the value of k is

• A. 1
• B. –1
• C. 0
• D. 2

Answer 1

Answer: (C)

0

Answer 2

If function is continuous at x = 0, then by the definition of continuity $f ( 0 ) = \lim _ { x \rightarrow 0 } f ( x )$

since $f ( 0 ) = k$. Hence, $f ( 0 ) = k = \lim _ { x \rightarrow 0 } ( x ) \left( \sin \frac { 1 } { x } \right)$

⇒ k = 0 (a finite quantity lies between –1 to 1) ⇒ k = 0.