Does not exist. Show that lim x → 2 (x-2)

LIMITS 3. Show that lim 1 does not exist x 0 x 4. Show that lim e 1/ x does not exist x 0 5. Show that lim [xl [xl 6. Let fx) be a function defined by f(x) Show that lim f(x) does not exist. 7. Evaluate lim f(x) (if it exists), where f(x) 8. Show that lim sin does not exist. 9. Find lim [x].

If f(x) = [x] – [x/4] , x ∈ R, where [x] denotes the greatest integer function, then : (1) lim f(x) (x→4-)exists but lim f(x) (x→4+) does not exist. (2) Both lim f(x) (x→4-) and lim f(x) (x→4+) exist but are not equal. (3) lim f(x) (x→4+) exists but lim f(x) (x→4-) does not exist. (4) f is continuous at x = 4.

Statement 1: If lim_(x rarr00)(f(x)+(sin x)/(x)) does not exist then lim_(x rarr00)f(x) does not exists. Statement 2:lim_(x rarr o)(sin x)/(x) exists and has value 1.

Statement - I: if lim_(x to 0)((sinx)/(x)+f(x)) does not exist, then lim_(x to 0)f(x) does not exist. Statement - II: lim_( x to 0)(sinx)/(x)=1

Statement -1 : lim_(xrarralpha) sqrt(1-cos 2(x-alpha))/(x-alpha) does not exist. Statement-2 : lim_(xrarr0) (|sin x|)/(x) does not exist.

Statement -1 : lim_(xrarralpha) sqrt(1-cos 2(x-alpha))/(x-alpha) does not exist. Statement-2 : lim_(xrarr0) (|sin x|)/(x) does not exist.

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.

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.

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.

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.