Which of the following function(s) can be defined continuously at `x = 0 ?` `f(x)=1/(1+2^cotx)`

Which of the following function(s) defined below has/have single point continuity.f(x)=[1, if x in Q and 0 if x!in Q

A function f RrarrR is defined as f(x)=x^(2) for xge0 and f(x)=-x for xlt0 consider the following statements in respect to the above function 1. the function is continuous at x = 0. 2. the function is differentiable at x = 0 which of the above function is/are continuous?

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

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

Is the function defined by f(x)={x+5, if x 1 a continuous function?

Is the function f defined by f(x)={{:(x , ifxlt=1),( 5, ifx >1):} continuous at x = 0? A t x = 1? A t x = 2?

Is the function f defined by f(x)={{:(x, if x le 1),(5, if x gt 1):} continuous at x = 0? At x = 2 ?

Show that the function 'f' defined as follows, is continuous at x = 2, but not differentiable there at: f(x) = {:{(3x-2,0 2):}

Is the function f defined by {{:(x," if "x le 1),(5," if "x gt 1):} continuous at x= 0? At x=1? At x=2?.