फलन `f(x)=1/(2+x) "की" x = 2 ` पर दक्षिण पक्ष ( Right hand limit) तथा वाम पक्ष सीमा ( Left hand limit ) ज्ञात कीजिए ।

The right hand limit of the funtion f(x) = 4

Statement-1 : lim_(x to 0) (sqrt(1 - cos 2x))/(x) at (x = 0) does not exist. Statement -2 :Right hand limit != Left hand limit i) Statement - 1 is True, Statement-2 is True, Statement-2 is a correct explanation for statement-1 ii)Statement-1 is True, Statement-2 is True, Statement-2 is Not a correct explanation for statement-1 iii)Statement-1 is True, Statement-2 is False iv)Statement -1 is False, Statement-2 is True

If f(x)=(1)/(1+e^(-(1)/(x))),x!=0 and 0,x=0 then at x=0 (A) right hand limit of f(x) exists but not left-hand limit (B) limit of f(x) exists but not but not right-hand limit (C) both limits exists but are not equal (D) both limits exist and are equal

The left hand limit of the function f(x)=4

Let f(x)=(x sin(x-[x]))/(x-1) .Then the right hand limit of f at x=1 is

Statement-1 : lim_(x to 0) (sqrt(1 - cos 2x))/(x) at (x = 0). Right and limit != hand limit

Let {x} denote the fractional part of x and f(x) = (cos^(-1) (1-{x}^2) sin^(-1)(1-{x}))/(({x})-{x}^3), x ne 0 . If L and R respectively denotes the left hand limit and the right hand limit of f(x) at x = 0 , then frac{32}{pi^2} (L^2+R^2) is equal to ____________.

In a function f : [-2a, 2a] rarr R is an odd function such that f(x) = f(2a - x) for x in [a, 2a] and the left hand derivative at x = a is 0, then find the left hand derivative at x = -a,

If f(x)={{:(2x+3"if", x le0),(3(x+1)"if",x gt theta):} Find left and right hand limits and choose whether f(x) has limit at the point x=0 .

if f(x)={{:(x^(2), if x le),(x, if1 lt x le2),(x-3,if x gt2):} Find the left and right hand limits and check wheather f(x) has limit at the point x=1:2