Question

In order that the function f(x) = (x + 1)^cotx is continuous at x = 0, f(0) must be defined as

• A. 0
• B. e
• C. $\frac{2}{3}$
• D. None of these

Answer 1

Answer: (B)

e

Answer 2

$\lim _ { x \rightarrow 0 } f ( x ) = \lim _ { x \rightarrow 0 } ( x + 1 ) ^ { \cot x }$(1^∞ form)

or $\lim _ { x \rightarrow 0 } f ( x ) = \lim _ { x \rightarrow 0 } \left[ ( 1 + x ) ^ { 1 / x } \right] ^ { \frac { x } { \tan x } } = e ^ { 1 }$ ⇒ f(0) = e