No, $\frac{0}{∞}$ is Not considered Indeterminate form. Because any limit that gives rise to this form will converges to Zero.
See, Not every undefined algebraic expression corresponds to an indeterminate form. For instance, $∞^∞$, $0^∞$, $1/∞$, $1/0$
etc are Not considered as Indeterminate form.
Why $\frac{0}{∞}$ is Not an Indeterminate Form
Proof :
Let the Expression be $\lim_{} \frac{f}{g}$.
We will have Two cases. One in which we will fix the numerator and we will apply limit on denominator. And in other case,
we will fix the denominator and we will apply limit on numerator .
Case 1 : Fix $f=0$ and let $g$ approach to infinity.
So, We have $\lim_{g \rightarrow ∞} \,\, \frac{0}{g}$
And We can solve it. We will have $\lim_{g \rightarrow ∞} \,\, \frac{0}{g}$ = 0
Case 2 : Fix $g=∞$ and let $f$ approach to zero.
So, We have $\lim_{f \rightarrow 0} \,\, \frac{f}{∞}$
And We can solve it. We will have $\lim_{f \rightarrow 0} \,\, \frac{f}{∞}$ = 0
So, We can see, In both cases, limit that gives rise to this form will converges to Zero.
Now, Let me pick any Indeterminate form and Prove it to you that Why that limit is called Indeterminate :
Why $\frac{0}{0} $ is an Indeterminate Form
Proof :
Let the Expression be $\lim_{} \frac{f}{g}$.
We will have Two cases. One in which we will fix the numerator and we will apply limit on denominator. And in other case,
we will fix the denominator and we will apply limit on numerator .
Case 1 : Fix $f=0$ and let $g$ approach to Zero.
So, We have $\lim_{g \rightarrow 0} \,\, \frac{0}{g}$
And We can solve it. We will have $\lim_{g \rightarrow 0} \,\, \frac{0}{g}$ = 0
Case 2 : Fix $g=0$ and let $f$ approach to Zero.
So, We have $\lim_{f \rightarrow 0} \,\, \frac{f}{0}$
And We can solve it. We will have $\lim_{f \rightarrow 0} \,\, \frac{f}{0}$ = $+∞ \,\,or -∞$
So, We can see, For any limit of the Form $\frac{0}{0}$, We have Three different results. Hence, It is Indeterminate form.
