[" Let "f(x)={[(x-1)sin(1)/(x-1),x!=1],[0],x=1],[[" (1) "f" is differentiable at "x=0" and at "x=1," (2) "f" is dif "," (2) "f" is dif "],[" (3) fis differentiable at "x=1" but not at "x=0," (4) "f" is ne "]]

Let f(x)={(x-1)sin1/(x-1)if\ x!=1 0,\ if\ x=1 . Then which one of the following is true? (a) f is differentiable at x=0\ and at \ x-1 (b) f is differentiable at x=0\ but not at \ x=1 (c) f is differentiable at x=0 nor at x=1 (d) f is differentiable at x=1\ but not at \ x=0

If a function f(x) is defined as f(x) = {{:(-x",",x lt 0),(x^(2)",",0 le x le 1),(x^(2)-x + 1",",x gt 1):} then a. f(x) is differentiable at x = 0 and x = 1 b. f(x) is differentiable at x = 0 but not at x = 1 c. f(x) is not differentiable at x = 1 but not at x = 0 d. f(x) is not differentiable at x = 0 and x = 1

Let f(x)={{:(,x^(n)sin\ (1)/(x),x ne 0),(,0,x=0):} Then f(x) is continuous but not differentiable at x=0 . If

Let f(x)={{:(,x^(n)"sin "(1)/(x),x ne 0),(,0,x=0):} Then f(x) is continuous but not differentiable at x=0. If

Show that the functions f (x) = x ^(3) sin ((1)/(x)) for x ne 0, f (0) =0 is differentiable at x =0.

Let f(xy)=f(x)f(y)AA x,y in R and f is differentiable at x=1 such that f'(1)=1 Also,f(1)!=0,f(2)=3. Then find f'(2)

If f(x)={'x^2(sgn[x])+{x},0 Option 1. f(x) is differentiable at x = 1 Option 2. f(x) is continuous but non-differentiable at x = 1 Option 3. f(x) is non-differentiable at x = 2 Option 4. f(x) is discontinuous at x = 2

If f(x)=x sin ""1/x"for "x ne 0, f(0)=0" then at x"=0, f(x) is