# 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 $$m0$$ $$\hspace{10mm}$$ (3) $$\frac{a_0}{b_0}$$ (D) if \(m

Note: For example, if (A) correctly matches (1), (B) with (2), (C) with (3), and (D) with (4), then answer as 1234.

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