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

Question

In order that the function f(x) = (x + 1)1/x is continuous at x = 0 , f(0) must be defined as (A) f(0) = 0  (B) f(0) = e  (C) f(0) = (1/e) (D) f(0) = 1

Tardigrade Admin · Accepted Answer

displaystyle limx→0 f(x) = f(0)= displaystyle lim x→ 0 (1+x)1/x = e

Q. In order that the function $f (x) = (x + 1)^{1/ x}$ is continuous at $x = 0, f (0)$ must be defined as

$f (0) = 0$

$f (0) = e$

$f (0) = \frac{1}{e}$

$f (0) = 1$

$x \to 0 lim f (x) = f (0) = x \to 0 lim (1 + x)^{1/ x} = e$

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

f(0)=0

f(0)=e

f(0)=e1​

f(0)=1