Which of the following functions is/are discontinuous at `x=1?` `f(x)=1/(1+2^(t a n x))` `g(x)=(lim)_(xvecoo)1/(1+n in s^2(pix))` `h(x)=2^-2^(((1/(1-x)))),x!=1a n dh(1)=1` `varphi(x)=(x-1)/(|x-1|+2(x-1)^2),x=1a n dvarphi(1)=1`

Options

A. `f(x)=(1)/(1+2^(tanx))`
B. `g(x)=underset(n rarroo)(lim)(1)/(1+n sin^(2)(pix))`
C. `h(x)=2^(-2^(((1)/(1-X)))),x ne 1 andh(1)=1`
D. `phi(x)=(x-1)/(|x-1|+2(x-1)^(2)),x ne 1 and phi(1)=1`

Answer

A

Explanation

(a) Clearly, f(x) is continuous at x = 1.
(b) `g(1^(+))=0,g(1)=1rArrg(x)` is discontinuous at x = 1
(c) `h(1^(+))=1 and h(1^(-))=0rArr h(x)` is discontinuous at x = 1
(d) `phi(1^(+))=1 and phi(1^(-))=-1rArr phi(x)` is discontinuous at x = 1