For what values of p does the `Lim_(x to 1) f(x)` exist , where f is defined by the rule
`f(x) = {:{(2px+3," if " x lt 1 ),(1 - px^(2)," if "x gt 1):}`

Find all the points of discontinuity of the function f(x) defined by f(x) = {:{(x+1, if x lt 1), (1 , if x =1), (x-1, if x gt1):}

Examine the differentiability of f, where f is defined by f(x)={{:(1+x, if x le 2),(5-x,ifx gt 2):} at x = 2 .

Discuss the continuity of the function f, where f is defined by f(x)={{:(-2, ifxlt=-1),( 2x , if-1 1):}

Does Lim_(x to 0 ) f(x) exist if f(x) = {:{(x," when "x lt 0 ),(0 ," when " x = 0 ),(x^(2)," when " x gt 0):}

lim_(x to -1)f(x) exists, find c given f(x)={{:(x+2,x le -1),(cx^(2), x gt -1)}

Find lim_(x to 0) f(x) , where f(x) = {{:(x -1,x lt 0),(0,x = 0),(x =1,x gt 0):}

If a function f(x) is defined as f(x) = {{:(-x",",x lt 0),(x^(2)",",0 le x le 1),(x^(2)-x + 1",",x gt 1):} then

Calculate lim_(x to 0) f(x) , where f(x) = (1)/(x^(2)) for x gt 0

Find lim_(x to 1) f(x) , where f(x) = {{:(x + 1, x != 1),(0, x = 1):}}

Let f_(1):R to R, f_(2):[0,oo) to R, f_(3):R to R and f_(4):R to [0,oo) be a defined by f_(1)(x)={{:(,|x|,"if "x lt 0),(,e^(x),"if "x gt 0):}:f_(2)(x)=x^(2),f_(3)(x)={{:(,sin x,"if x"lt 0),(,x,"if "x ge 0):} and f_(4)(x)={{:(,f_(2)(f_(1)(x)),"if "x lt 0),(,f_(2)(f_(1)(f_(1)(x)))-1,"if "x ge 0):} then f_(2) of f_(1) is