" (iv) "f(x)={[x sin(1)/(x)," if "x!=0],[0," if "x=0]quad " at "x=0

Show that the function f(x) given by f(x)={:{(x" sin "(1)/(x)", if "x!=0),(0" , if "x=0):} is continuous at x =0

Discuss the differentiability of f(x)={x^2sin(1/x),\ \ \ \ x!=0 ; 0 if x=0 at x=0

f(x)={(x^2 sin (1/x), xne0 ),(0, x=0):} at x=0

f(x) = {{:(x^(2)sin'1/x, if x ne 0),(0, if x = 0):} at x = 0 .

f(x) = {{:(x^(2)sin'1/x, if x ne 0),(0, if x = 0):} at x = 0 .

If f(x)={(x"sin"(1)/(x),"when "x ne 0),(0,"when "x =0):} then at x = 0, the function f(x) is -

Test the continuity of the following functions at indicated points : f(x) = {{:((x) "sin" 1/(x)"," ,x != 0),(0",", x = 0):} at x = 0

Prove that f(x)={x sin((1)/(x)),x!=0,0,x=0 is not differentiable at x=0

Test differentiability and continuity of the following functions. f(x) = {(x sin (1/x), x ne 0), (0, x = 0) :} at x = 0.

Test the continuity of the following functions at indicated points : f(x) = {{:(x^2 "sin" 1/x"," ,x != 0),(0",", x = 0):} at x = 0