If f is derivable function of x, then`underset(hto0)("lim")(f(x+h)-f(x-h))/(h)=`

If a function f is differentiable at x= a, then underset(hto0)("lim")(f(a-h)-f(a))/(h)=

If f(x) is a differentiable function of x then lim_(h rarr0)(f(x+3h)-f(x-2h))/(h)=

(d)/(dx)[underset(hto0)("lim")((x+h)^(4)-x^(4))/(h)]=

If f is a differentiable function of x, then lim_(h rarr0)([f(x+n)]^(2)-[f(x)]^(2))/(2h)

(d^(2))/(dx^(2))[underset(hto0)("lim")((x+h)^(4)-x^(4))/(h)]=

Left hand derivative and right hand derivative of a function f(x) at a point x=a are defined as f'(a^-)=lim_(h to 0^(+))(f(a)-f(a-h))/(h) =lim_(hto0^(+))(f(a+h)-f(a))/(h) andf'(a^(+))=lim_(h to 0^+)(f(a+h)-f(a))/(h) =lim_(hto0^(+))(f(a)-f(a+h))/(h) =lim_(hto0^(+))(f(a)-f(x))/(a-x) respectively. Let f be a twice differentiable function. We also know that derivative of a even function is odd function and derivative of an odd function is even function. The statement lim_(hto0)(f(-x)-f(-x-h))/(h)=lim_(hto0)(f(x)-f(x-h))/(-h) implies that for all x"inR ,

Let fRtoR be a function we say that f has property 1 if underset(hto0)(lim)(f(h)-f(0))/(sqrt(|h|)) exist and is finite. Property 2 if underset(h to 0)(lim)(f(h)-f(0))/(h^(2)) exist and is finite. Then which of the following options is/are correct?