Match the limit
Calculus
Level
3
Let
\[f(x)=\frac{a_0 x^{m}+a_1 x^{m+1}+\cdots +a_k x^{m+k}}{b_0 x^{n}+b_1 x^{n+1}+\cdots +b_ l x^{n+l}},\]
where \(a_0 \neq 0, b_0 \neq 0,\) and \(m,n \in \mathbb N.\)
Then given (A), (B), (C), or (D), \(\displaystyle\lim_{x\rightarrow 0}f(x)\) equals which of (1), (2), (3), and (4)?
Match the columns:
| Column-I | Column-II |
| (A) if \(m>n\) | (1) \(\infty\) |
| (B) if \(m=n\) | (2) \(-\infty\) |
| (C) if \(m<n,\) \(n-m\) is even, and \(\frac{a_0}{b_0}>0\) \(\hspace{10mm}\) | (3) \(\frac{a_0}{b_0}\) |
| (D) if \(m<n,\) \(n-m\) is even, and \(\frac{a_0}{b_0}<0\) \(\hspace{10mm}\) | (4) \(0\) |
Note: For example, if (A) correctly matches (1), (B) with (2), (C) with (3), and (D) with (4), then answer as 1234.
by
Yash Dev Lamba