Question

If $\lim_{x \rightarrow 3^{+}}f(x) = 0$ is continuous at x = 0, then the value of ‘a’ will be

• A. 8
• B. –8
• C. 4
• D. None of these

Answer 1

Answer: (A)

8

Answer 2

$\lim _ { x \rightarrow 0 ^ { - } } f ( x ) \lim _ { x \rightarrow 0 ^ { - } } \left( \frac { 2 \sin ^ { 2 } 2 x } { ( 2 x ) ^ { 2 } } \right) 4 = 8$

and $\lim _ { x \rightarrow 0 ^ { + } } f ( x ) = \lim _ { x \rightarrow 0 ^ { + } } [ ( \sqrt { 16 + \sqrt { x } } ) + 4 ] = 8$

Hence $a = 8$.