If `f(x)=|x-2|` write whether `f\ '\ (2)` exists or not.

If f(x)=|x+100|+x^(2) , test whether f'(100) exists.

If f(x) = |x+100|+x^2 , test whether f'(-100) exists.

If f(x)= |x+100| + x^(2) , test whether f^( )(-100) exist.

Draw the graph of y=f(x)=(x^(2))/(x) and from the graph examine whether underset(xrarr0)"lim"f(x) exists or not .

If f(x) is an odd function,then write whether f'(x) is even or odd.

If f(x) is an even function,then write whether f'(x) is even or odd.

A function f (x) is defined as follwos : f(x){:(=2x+1," when "xle 1),(= 3-x," when "xgt1):} Examine whether underset(xrarr1)"lim"f(x) exists or not.

The function f(x) is defined as follows: f(x)=2-3x, when x =0 Evaluate lim_(x rarr0^(+))f(x),lim_(x rarr0^(-))f(x) and hence state whether lim_(x rarr0)f(x) exists or not.