Question

If f (x) = $\lbrack(1–\sin x)^{2}f(x)\rbrack^{\frac{1}{\sin x–1}}$ is to be made continuous at x = 1, then f (1) should be equal to –

• A. e²
• B. e
• C. 1/e
• D. e^–2

Answer 1

Answer: (A)

e²

Answer 2

Q f(1) = f(1⁺)

e$\lim _ { h \rightarrow 0 }$ $\frac { \tan ( \pi / 4 + \ln ( 1 + \mathrm { h } ) - 1 ) } { \ln ( 1 + \mathrm { h } ) }$ $\frac { 0 } { 0 }$

e$\lim _ { h \rightarrow 0 }$ $\frac { \sec ^ { 2 } ( \pi / 4 + \ln ( 1 + \mathrm { h } ) \cdot 1 / 1 + \mathrm { h } ) } { 1 / 1 + \mathrm { h } }$

f(1) = e²