Find whether the limit of f(x) exists or not at x = 3 , where `f(x)={{:(x+2,"if " -1ltxle3),(x^(2),"if "3ltxlt5):}`

Find whether the limit of f(x) exists or not at x = 3, where f(x) = {(x + 2, if - 1 < x le 3),(x^2, if 3 < x < 5):}

If f(x)={{:(5x-4",",0ltxle1),(4x^(2)+3ax",",1ltxlt2):}

Find the left and right hand limits of the function at the point 'a' mentioned against them. Hence check whether the function have limits at those points. f(x)={{:(x+2" if "-1ltxle3),(x^(2)" if "3ltxlt5):},a=3

Examine the continuity of f(x) at x=1/2 where f(x)={{:(1/2-x", "0lexlt1/2),(1", "x=1/2),(3/2-x", "1/2ltxle1):}

int_(1)^(3)f(x)dx , equals where f(x)={{:(2x+1","," when "1lexle2),(x^(2)+1","," when "2ltxle3):}

Find a if f’ (a) =0, where f(x) =x^3- 3x^2 + 3x-1 .

Find all points of discontinuity of f, where f is defined by f(x)={:{(|x|+3", if "xle-3),(-2x", if "-3ltxlt3),(6x+2", if "xge3):}