Graph of the function `f(x)={[x+2,xge1],[x+1,xlt1]}` is

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?

Draw the graph of the function f(x)={{:(x^(2)",", " when ", xlt0),(x",", " when " , 0le x le1),(1//x",", " when " , 1 le x lt oo.):}

Show that the function f(x)={:{(x^2+2", " xge1),(2x+1", " x lt 1 ):} is always differentiable at x=1

Draw the graph of the function f(x)=x-|x-x^(2)|,-1<=x<=1 and discuss the continuity or discontinuity of f in the interval -1<=x<=1

Discuss the continuity of the function f(x)={x , 0lt=x<1//2 12 , x=1//2 1-x , 1//2

Draw the graph of the function f(x) = (1+1/x)^(2)

Find the complete set of values of alpha for which the function f(x) = {(x+1,xlt1 alpha , x =1 , is strictly increasing x=1 x^(2)-x+3,xlt1

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