Let `f(x)=(1-x(1+|1-x|))/(|1-x|)cos(1/(1-x))` for `x!=1.` Then: (A)`(lim)_(n->1^-)f(x)` does not exist (B)`(lim)_(n->1^+)f(x)` does not exist (C)`(lim)_(n->1^-)f(x)=0` (D)`(lim)_(n->1^+)f(x)=0`

If f(x)=(|x-1|)/(x-1) prove that lim_(x rarr1)f(x) does not exist.

Consider the following graph of the function y=f(x). Which of the following is//are correct? (a) lim_(xto1) f(x) does not exist. (b) lim_(xto2)f(x) does not exist. (c) lim_(xto3) f(x)=3. (d)lim_(xto1.99) f(x) exists.

If f(x)=xs in(1/x),x!=0 then (lim_(x rarr0)f(x)= a.1b*-1 c.0 d.does not exist

Let f(x)=lim_(ntooo)(1-x^n)/(1+x^n) . Then

Which of the following statement(s) is (are) INCORRECT ?. (A) If lim_(x->c) f(x) and lim_(x->c) g(x) both does not exist then lim_(x->c) f(g(x)) also does not exist.(B) If lim_(x->c) f(x) and lim_(x->c) g(x) both does not exist then lim_(x->c) f'(g(x)) also does not exist.(C) If lim_(x->c) f(x) exists and lim_(x->c) g(x) does not exist then lim_(x->c) g(f(x)) does not exist. (D) If lim_(x->c) f(x) and lim_(x->c) g(x) both exist then lim_(x->c) f(g(x)) and lim_(x->c) g(f(x)) also exist.

Let f(x)=(lim)_(n->oo)(2x^(2n)sin1/x+x)/(1+x^(2n))\ then find :\ (lim)_(x->-oo)f(x)

Letf(x)={{:(x+1,", "if xge0),(x-1,", "if xlt0):}".Then prove that" lim_(xto0) f(x) does not exist.

Let f(x)=(sin^(-1)(1-{x})*cos^(-1)(1-{x}))/(sqrt(2{x})(1-{x})) then find lim_(x rarr0^(+))f(x) and lim_(x rarr0^(-))f(x)

Statement 1: If lim_(xto0){f(x)+(sinx)/x} does not exist then lim_(xto0)f(x) does not exist. Statement 2: lim_(xto0)((e^(1//x)-1)/(e^(1//x)+1)) does not exist.

Let f(x)=cos(x cos((1)/(x))) statement- -1:f(x) is discontinuous at x=0. Statement- 2: Lim -(x rarr0)f(x) does not exist.