Question

If ƒ(x) = $\frac{2}{3}$is a continuous function on (–π/6, π/6), then-

• A. a = 2/3, b = e²
• B. a =1/3, b = e^1/3
• C. a = 2/3, b = e^2/3
• D. None of these

Answer 1

Answer: (C)

a = 2/3, b = e^2/3

Answer 2

b = ƒ(0) = $\lim _ { x \rightarrow 0 ^ { + } }$ƒ(x) = $\lim _ { x \rightarrow 0 }$e^{tan 2x / tan 3x}

= $\lim _ { x \rightarrow 0 }$ = e^2/3,

Also, b = ƒ(0) = $\lim _ { x \rightarrow 0 }$ƒ(x)

= $\lim _ { x \rightarrow 0 }$= e^a

Therefore a = 2/3 & b = e^2/3.