Show that `f(x)={(x sin frac{1}{x}, xne0),(o,x=0):}`
is continuous at x=0

Show that f(x)={(xsinfrac{1}{x},xne0),(0,x=0):} is not differentiable x=0

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

Find the value of a such that the function f defined by f(x)={((sinax)/(sinx) if xne0),(1/a if x=0):} is continuous at x=0.

For what value of k, the function f(x)={{:((sin2x)/(x)", "x!=0),(k", "x=0):} is continuous 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

Show that the function f(x)={{:((sinx)/(x)+cosx", if "x!=0),(2", if "x=0):} is continuous at x=0 .

For what value of k, the function f(x)={((tan2x)/(x)", if "x!=0),(k", if "x=0):} is continuous at x=0 ?

Find the value of a such that the function f defined by f(x)={{:((sinax)/(sinx), "if", x ne 0),((1)/(a), "if", x=0):} is continuous at x=0

If a function f(x) is defined by f(x) = {((1+7x)^(1/x),when x!=0),(k,when x =0):} is continuous at x = 0, then what is the value of k.?

For what value of lambda ,is the function f(x)={(lambdax^2-2x,if xle0),(4x+1,ifx>0):} is continuous at x=0