How do you determine the limit of #sqrt(x-4)/(3x+5)# as x approaches negative infinity?
Notice that you have a square root in your numerator. This can complicate the usual process, so you'll need to take a few extra steps to make sure this works.
The first step is the same as usual: we're going to divide everything by the highest power, which in this case is
For the numerator, we have to make one small simplification to get the right number into the square root:
Now, we divide through and simplify:
Now, you just go ahead and take your limit:
Hope that helped :)