If the function ` g(x) {{:((e^(px) + log _(e) (1+4x)+q)/(x^(3))","x ne 0),(r"," x=0):}`
continuous at x=0 , then find the values of p,q and r.

If f(x)={{:(((5^(x)-1)^(3))/(sin((x)/(a))log(1+(x^(2))/(3)))",",x ne0),(9(log_(e)5)^(3)",",x=0):} is continuous at x=0 , then value of 'a' equals

Let f : R rarr R be defined as f(x) = {{:((x^(3))/((1-cos 2x)^(2)) log_(e)((1+2x e^(-2x))/((1-x e^(-x))^(2))),",",x ne 0),(alpha,",", x =0):} . If f is continuous at x = 0, then alpha is equal to :

If the function f(x)=((e^(kx)-1)tankx)/(4x^(2)),x ne 0 =16" "x=0 is continuous at x=0, then k= . . .

Prove that the function If f(x)={:{((x)/(1+e^(1//x)) ", " x ne 0),(" "0", " x=0):} is not differentiable

The value of k for which f(x)={{:(,[1+x(e^(-1//x^(2)))sin(1/(x^(4)))]^(e1//x^(2)),x ne 0),(,k,x=0):} is continuous at x=0, is

For the function f(x) = (log_(e )(1+x)-log_(e )(1-x))/(x) to be continuous at x = 0, the value of f(0) should be