`lim_(h rarr 0) (f(a+h) - f(a))/(h) =`

Let f be differentiable at x=0 and f'(0)=1 Then lim_(h rarr0)(f(h)-f(-2h))/(h)=

If is an even function such that lim_(h rarr 0) (f(h)-f(0))/(h) has some fininte non-zero value, then

Let f(x) = 3x^(10) - 7x^(8) + 5x^(6) - 21x^(3) + 3x^(2) - 7 . Then lim_(h rarr 0) (f(1-h)-f(1))/(h^(3) + 3h) equals :

Left hand derivative and right hand derivative of a function f(x) at a point x=a are defined as f'(a^-)=lim_(hrarr0^(+))(f(a)-f(a-h))/(h) =lim_(hrarr0^(+))(f(a+h)-f(a))/(h) andf'(a^(+))=lim_(hrarr0^(+))(f(a+h)-f(a))/(h) =lim_(hrarr0^(+))(f(a)-f(a+h))/(h) =lim_(hrarr0^(+)) (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. If f is even function, which of the following is right hand derivative of f' at x=a?

Left hand derivative and right hand derivative of a function f(x) at a point x=a are defined as f'(a^-)=lim_(hrarr0^(+))(f(a)-f(a-h))/(h) =lim_(hrarr0^(+))(f(a+h)-f(a))/(h) andf'(a^(+))=lim_(hrarr0^(+))(f(a+h)-f(a))/(h) =lim_(hrarr0^(+))(f(a)-f(a+h))/(h) =lim_(hrarr0^(+)) (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. If f is even function, which of the following is right hand derivative of f' at x=a?

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