`lim_(h->0)((x+h)^(x+h)-x^x)/h=`

lim_(h rarr0)((x+h)^(x+h)-x^(x))/(h)=

Evaluate the following lim_(hto0) ((x+h)^3-x^3)/h

Evaluate the following lim_(hto0)((x+h)^4-x^4)/h

Prove that lim_(x->0) (f(x+h)+f(x-h)-2f(x))/h^2 = f''(x)

Prove that lim_(x->0) (f(x+h)+f(x-h)-2f(x))/h^2 = f''(x) (without using L' Hospital srule).

Prove that lim_(x->0) (f(x+h)+f(x-h)-2f(x))/h^2=f''(x) (without using L' Hospital srule).

The value of lim_(h to 0) (f(x+h)+f(x-h))/h is equal to

the value of lim_(h to 0) (f(x+h)+f(x-h))/h is equal to

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 ,

If f(x)=(1)/(x), evaluate lim_(h rarr0)(f(x+h)-f(x))/(h)