Find `lim_(xrarr0)f(x)a n d(lim)_(x->1)f(x),""""w h e r e""""f(x)=[2x+3, xlt=0 3(x+1), x >0`

Find (lim)_(x->1)f(x),""w h e r e""f(x)=[x^2-1, xlt=1-x^2-1, x >1

Evaluate ("lim")_(x->0)f(x),\ w h e r e\ f(x)={(|x|)/x ,\ x!=0 , 0,\ x=0

Evaluate lim_(xrarr0) f(x) , where

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

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

lim_(xrarr0) (e^(tanx)-e^x)/(tanx-x)=

Find lim_(xrarr0) f(x) where f(x)={{:((x)/(|x|),xne0),(0,x=0):}

Evaluate : lim_(xrarr0)((1-x)^(n)-1)/(x)

Let f(x) is a function continuous for all x in R except at x = 0 such that f'(x) lt 0, AA x in (-oo, 0) and f'(x) gt 0, AA x in (0, oo) . If lim_(x rarr 0^(+)) f(x) = 3, lim_(x rarr 0^(-)) f(x) = 4 and f(0) = 5 , then the image of the point (0, 1) about the line, y.lim_(x rarr 0) f(cos^(3) x - cos^(2) x) = x. lim_(x rarr 0) f(sin^(2) x - sin^(3) x) , is

lim_(xrarr0)((1-e^x)sin x )/(x^2+x^3) is equal to