# Match the Limit

**Calculus**Level 4

Let \[f(x)=\frac{a_0 x^{m}+a_1 x^{m+1}+.....+a_k x^{m+k}}{b_0 x^{n}+b_1 x^{n+1}+.....+b_ l x^{n+l}}\]

where \(a_0 \neq 0\) , \(b_0 \neq 0\) and \(m,n \in \mathbb N\) then \(\displaystyle\lim_{x\rightarrow 0}f(x)\) is equals to

**Match the Column:-**

Column-I | Column-II |

(A) If \(m>n\) | (1) \(\infty\) |

(B) If \(m=n\) | (2) \(-\infty\) |

(C) If \(m<n\) and \(n-m\) is even , \(\frac{a_0}{b_0}>0\) | (3) \(\frac{a_0}{b_0}\) |

(D) If \(m<n\) and \(n-m\) is even , \(\frac{a_0}{b_0}<0\) | (4) \(0\) |

**Note:-**
For example, if

(A) correctly matches (1),

(B) with (2),

(C) with (3),

(D) with (4)

then answer as 1234.