Match the limit

Calculus Level 2

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.

The answer is 4312.

3 solutions

Sudhanshu Stie
May 18, 2018

See image for solution.
I don't have a proper knowledge about Latex thats why i upload the image. Download
Hey there I am not a mathematician . If I have done anything wrong Please let me know.

Pranav Rao
Mar 16, 2016

I think we say limit of function exists at a point when both left hand limit and right hand limit of that function are finite and are equal. So for case 3 and 4 does the limit exist at x =0?

Terrell Bombb
Nov 2, 2016

1st case simplifies to lim(x->0)ax/b = 0

2nd case simplifies to lim(x->0) (a 0*x^m-1)/(b 0*x^m-1) = a 0/b 0

3rd case simplifies to lim(x->0) a 0/b 0*x^2 = +infinity

4th case takes the remaining option

Can u explain elaborately

Arun Krishna AMS - The Joker - 4 years ago

@Terrell Bombb please explain how you simplified

Saksham Jain - 3 years, 7 months ago

you really helped me sooo fucking much dude well done.

Albert Bustos - 3 years, 4 months ago

Match the limit

The answer is 4312.

3 solutions

1 pending report

Vote up reports you agree with