Question

If f(x) = $\sqrt{\frac{5}{2}}$ when x ≠ π/2 and f(π/2) = λ then f(x) will be a continuous function at x = π/2 when λ is –

• A. 1/8
• B. ¼
• C. ½
• D. None

Answer 1

Answer: (A)

1/8

Answer 2

Q f(x) is continuous at x = π/2

∴ $\lim _ { x \rightarrow \pi / 2 }$ $\frac { 1 - \sin \mathrm { x } } { ( \pi - 2 \mathrm { x } ) ^ { 2 } }$ = f(π/2)

applying D.L. $\lim _ { x \rightarrow \pi / 2 }$ $\frac { - \cos x } { 2 ( \pi - 2 x ) ( - 2 ) }$ = λ

again D.L = $\lim _ { x \rightarrow \pi / 2 }$ $\frac { \sin x } { - 4 . ( - 2 ) }$ = λ ⇒ $\frac { 1 } { 8 }$ = λ