We note first we have a fractional function here that we can write:

with,

,.

We know that n>m, this means that

and

. This means that

We need to know that:

,

 We also know that from the properties of the exponentials that: 

.

Now we need to note that since n<m, we have n-m<0

and therefore:

.

This means that :

.

Recall that for all real numbers we have:

, from which we deduce that: 

.

We know that:

.

Therefore:

.

Simplifying the above expression gives:

For the function , there is an asymptote at .

The graph approaches to positive infinity as  approaches zero from the right side of the graph, and negative infinity as  approaches zero from the left.

Therefore, the limit of  from the left approaches to .

When finding horizontal asymptotes, there are 3 conditions / rules to follow.

1) if the leading terms of the numerator and denominator are of the same degree, then the HA is equal to the ratio of the coefficients of the leading terms

2) if the leading term of the denominator is of a higher degree than the leading term of the numerator, then the HA is 

3) if the leading term of the numerator is of a higher degree than the leading term of the denominator, then there is no horizontal asymptote (or it is undefined)

This question falls into condition 1, and therefore the horizontal asymptote is .

When finding horizontal asymptotes, there are 3 conditions / rules to follow.

1) if the leading terms of the numerator and denominator are of the same degree, then the HA is equal to the ratio of the coefficients of the leading terms

2) if the leading term of the denominator is of a higher degree than the leading term of the numerator, then the HA is 

3) if the leading term of the numerator is of a higher degree than the leading term of the denominator, then there is no horizontal asymptote (or it is undefined)

This question falls into condition 2, and therefore the horizontal asymptote is .

When finding horizontal asymptotes, there are 3 conditions / rules to follow.

1) if the leading terms of the numerator and denominator are of the same degree, then the HA is equal to the ratio of the coefficients of the leading terms

2) if the leading term of the denominator is of a higher degree than the leading term of the numerator, then the HA is 

3) if the leading term of the numerator is of a higher degree than the leading term of the denominator, then there is no horizontal asymptote (or it is undefined)

This question falls into condition 3, and therefore there is no horizontal asymptote / the asymptote is undefined.

The denominator is not valid and does not exist at .  There is an asymptote at .  However, the question asked for the limit when the graph is approaching  from the right side.  

Following the curve of the graph of , the range will approach negative infinity when we follow the graph from the right end of .

Therefore, the answer is: 

The easiest way to determine this limit is to reduce tangent to its component parts.

As x approaches  from the left, the numerator approaches  while the denominator approaches , meaning that the limit is positive infinity. 

Therefore,

The denominator equals zero only where .