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:-

(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.


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