Consider the following in respect of the function
`f(x)={{:(2+x","xge0),(2-x","xlt0):}`
1. `underset(xto1)limf(x)` does not exist.
2. f(x) is differentiable at x=0
3. f(x) is continuous at x=0
Which of the above statements is /aer correct?

Consider the following in respect of the function f(x)={{:(2+x,xge0),(2-x,xlt0):} 1. underset(xrarr1)limf(x) does not exist 2. f(x) is differentiable at x = 0 3. f(x) is continuous at x = 0 Which of the above statements is / are correct?

Consider the following in respect of the function f(x)={{:(2+x","xge0),(2-x","xlt0):} 1. lim_(x to 1) f(x) does not exist. 2. f(x) is differentiable at x=0 3. f(x) is continuous at x=0 Which of the above statements is /aer correct?

Consider the following in respect of the function f(x)={2+x, x>=0; 2-x, x 1) f(x) does not exist. (2) f(x) is differentiable at x=0 (3) f(x) is continuous at x=0 Which of the above statements is/are correct? (a) 1 only (b) 3 only (c) 2 and 3 only (d) 1 and 3 only

Discuss the continuity of the function : f(x)={{:(x",if "xge0),(x^(2)",if "xlt0):}

If f(x)={{:((x-|x|)/(x)","xne0),(2", "x=0):}, show that lim_(xto0) f(x) does not exist.

Consider the following statements in respect of a function f(x) I. f(x) continuous at x = a. if underset(xrarra)limf(x) exists II. If f(x) is continuous at a point, then (1)/(f(x)) is also continuous at the point. Which of the above statements is/are correct?

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

Consider the following statements in respect of the function f(x)=sin((1)/(x)) for xne0 and f(0)=0 1. underset(xrarr0)lim f(x) exists 2. f(x) is continuous at x = 0 Which of the above statements is/are correct?

if f(x)={{:(2+x,xge0),(2-x,xlt0):} then lim_(x to 0) f(f(x)) is equal to