Let `f(x)={(1+3x)^(1/x), x != 0e^3,x=0` Discuss the continuity of `f(x)` at (a) `x=0,` (b) `x=1`

Discuss the continuity of f(x)={|x|cos((1)/(x)),quad x!=00,quad x=0 at x=0

Discuss the continuity of f(x) ={:{(cos""(1)/(x)", "x ne 0),(" "1", " x= 0):},

Discuss the continuity of f(x) ={:{(sin""(1)/(x)", "x ne 0),(" "1", " x= 0):},

Let f(x)={[((e^(3x)-1))/(x),,x!=0],[3,,x=0]} then 2f'(0) is

Is f(x)=(1+x)^((1)/(x)), when x!=0=e, when x=0 continuous at x=0?

Let f(x)=(xe)^((1)/(|x|)+(1)/(x));x!=0,f(0)=0, test the continuity & differentiability at x=0

f(x)={(x^(2))/(2),0<=x<1 and 2x^(2)-3x+(3)/(2),1<=x<=2 Discuss the continuity of f,f; and f' on [0,2]

Let f(x) = {{:(x^(2)/2", "0 lexlt1),(2x^(2)-3x+3/2", "1lexle2):} Discuss the continuity of f, f' and f'' on [0, 2].