Indeterminate form from calculus What do we mean by Indeterminate form  ?
can we show $0/0$ anything as we wish 
i mean is it not unique 
there can be several answers for it
 A: No, obtaining an indeterminate form does NOT mean that "anything goes" for evaluating a limit, or that the limit is not unique. It simply means that "more work needs to be done." For example, one might need L'Hopital.
For example, if we have the "trivial" situation where $\lim_{x \to 0} \dfrac{x^2}{x^4}$, it is at first glance, of indeterminate form $\frac 00$. But we can easily modify the limit: $$\underbrace{\lim_{x \to 0} \dfrac {x^2}{x^4}}_{\text{indeterminate}} = \underbrace{\lim_{x \to 0} \dfrac 1{x^2}}_{\text{NOT indeterminate}}\to \quad +\infty$$
See the Wikipedia entry on indeterminate form, with respect to taking limits. See also the list of seven indeterminate forms in that same Wikipedia entry. You'll also see the examples of several functions for which the limit evaluates to an indeterminate form and what work is done to obtain an indeterminate form.
A: If you talk about $\frac{0}{0}$ in algebra, then it is undefined.
If you talk about $\frac{0}{0}$ in Calculus, then it means that you need to go further and find what the limit is. 
For example $\displaystyle \lim_{x \to 1} \frac{x^3-1}{x^2-1} = \frac{0}{0}$.
But if you write $(x^3-1)=(x-1)(x^2+x+1)$ and $(x^2-1)=(x-1)(x+1)$ then you'll see that 
$$\displaystyle \lim_{x \to 1} \frac{x^3-1}{x^2-1} = \lim_{x \to 1}\frac{(x-1)(x^2+x+1)}{(x-1)(x+1)}=\lim_{x \to 1} \frac{x^2+x+1}{x+1}=\frac{3}{2}$$.
You can do the same with $\displaystyle \lim_{x \to 1}\frac{x^4-1}{x^2-1}=\frac{0}{0}$
$$\lim_{x \to 1} \frac{x^4-1}{x^2-1} = \lim_{x \to 1} \frac{(x^2+1)(x^2-1)}{x^2-1}=\lim_{x \to 1} x^2+1 = 2 $$
So, $\frac{0}{0}$ in calculus is indeterminate in the sense that you need to do more work and see what it really is. Because when we talk about $\frac{0}{0}$ we mean that two infinitesimals(infinitely small numbers) are divided, so even though they are very very small, but they are still non-zero numbers and it's meaningful to talk about whether their ratio approaches some real number or not.
