Evaluate the left-and right-hand limits of the function defined by `f(x)={(1+x^2, 0lex<1), (2-x ,x gt1):}` at `x=1` Also, show that `lim_(xrarr1)f(x)` does not exist

Evaluate the left-and right-hand limits of the function f(x)={(|x-4|)/(x-4),x!=4 0,x=4a tx=4

The right hand limit of the funtion f(x) = 4

The left hand limit of the function f(x)=4

Evaluate the left-hand and right-hand limits of the following function at x = 1 : f(x)={{:(5x-4",", "if "0 lt x le 1), (4x^(2)-3x",", "if "1 lt x lt 2.):} Does lim_(x to 1)f(x) exist ?

A function f defined by f(x)=In(sqrt(x^(2)+1-x)) is

Find the domain of the function f(x) defined by f(x)=sqrt(4-x)+1/(sqrt(x^2-1)) .

Find the domain of the real function f(x) defined by f(x)=sqrt((1-|x|)/(2-|x|))

Evaluate right-handed limit of the function : f(x)={{:(abs(x-3)/(x-3)",",x ne 3), (" 0,", x=3):} at x = 3.