# Are all limits solvable without L’Hôpital Rule or Series Expansion

Is it always possible to find the limit of a function without using L’Hôpital Rule or Series Expansion?

For example,

Yes if we know beforehand the limit exists.

For $L_1$:

For $L_2$:

For $L_3$:

For $L_4$:

For $L_5$:

Since you would consider binomial theorem as series expansion, if not well and good, if yes, then I’ll do:
Now let $\sqrt{1-5 x^2+4x^4}=\sum a_kx^k$, squaring both sides,
Now taking positive branch:

So:

For $L_6$: