Let ` f(x)= {:{ (x + a , x ge 1 ) , ( ax^(2) + 1, x lt 1) :}` then f(x) is derivable at x =1 , if

f(x) {{:(x + 1"," if x ge 1 ),(x^(2)+ 1"," if x lt 1):}

Let f(x)= {:{((x+a) , x lt1),( ax^(2)+1, xge1):} then f(x) is continuous at x =1 for

Let f(x) = {{:(( 2+x)",",if , x ge0), (( 2-x)",", if , x lt 0):} show that f(x) not derivable at x =0

Let f(x)={a x^2+1,\ \ \ \ \ x >1 , \ \ \ \ x+1//2,\ \ \ \ \ xlt=1 Then, f(x) is derivable at x=1 , if a=2 (b) b=1 (c) a=0 (d) a=1//2

Let f(x) = {{:( x, if , x ge 1),( x^(2), if , x lt 1):} is f a continuous function ? Why ?

Let f(x)={(tan^(-1)x, , |x|ge1),((x^(2)-1)/4, , |x|lt1):} then domain of f'(x) is

If f(x)={{:(,(x)/(1+|x|),|x|ge 1),(,(x)/(1-|x|),|x| lt 1):} then f(x) is

Let f(x)= {{:(1+ sin x, x lt 0 ),(x^2-x+1, x ge 0 ):}