Consider the function f(x)= begincases 1, text if x ≤ 0 2, text if x0 endcases some statements are given below based on the above function. Identify the correct combination of true (T) and false (F) of the given statements. (i) Left and right hand limit of the function is equal at x=0. (ii) Limit of the function does not exist at x=0. (iii) The left and right hand limit of f at 0 is 1 and 2 , respectively.

Question

Consider the function f(x)= begincases 1, text if x ≤ 0 2, text if x>0 endcases some statements are given below based on the above function. Identify the correct combination of true (T) and false (F) of the given statements. (i) Left and right hand limit of the function is equal at x=0. (ii) Limit of the function does not exist at x=0. (iii) The left and right hand limit of f at 0 is 1 and 2 , respectively. (A) TTT (B) TFT (C) FTT (D) TTF

Tardigrade Admin · Accepted Answer

Using the language of left and right hand limits, we may say that the left (respectively right) hand limit of f at 0 is 1 (respectively 2). In particular the left and right hand limits do not coincide thus the limit of the function does not exist at x=0. We also refer to graph in solution 1 .