Home > Calculus > Determining Limits Algebraically

How do you determine the limit of #3/(x+1) # as x approaches -1?

Answer 1

Samantha Adkison

#lim_"x-> -1" 3/(x+1)# does not exist

First consider #lim_"x->-1" 3/(x+1)# from #x<-1# This limit #-> -oo#

Then consider #lim_"x->-1" 3/(x+1)# from #x> -1# This limit #-> +oo#

Hence the limit diverges.

This can be easily be seen from the graph of #3/(x+1)# in the region of #x=-1# below:

graph{3/(x+1) [-12.66, 12.64, -6.32, 6.34]}

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Scarlett Allison

To determine the limit of 3/(x+1) as x approaches -1, we can substitute -1 into the expression and evaluate it. By substituting -1 for x, we get 3/(-1+1), which simplifies to 3/0. However, division by zero is undefined in mathematics. Therefore, the limit of 3/(x+1) as x approaches -1 does not exist.

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.