For which value of d does the following limit exist?
lim x->d ln [ (x2-13x+30) / (x-d) ]
The Attempt at a Solution
I understand how to find limits when the limit goes to a real number, and has a variable in the function to solve for, but not when the limit goes to a variable.
I thought perhaps attempting to multiply the whole thing by (x+d)/(x+d)
For simplicity I figure we can ignore that natural log for now.
= (dx2 -13dx +30d +x3 -12x2 +30x) / (x2 + d2)
Which when simplified down gave me [ (-12x+47) / d ]
How do I go from here to solve for d though?
I tried subbing x as d, like I would solving for a limit normally, however this is on a program that provides instant feedback and ln(35) is incorrect.
Rather than the answer, as this is an assignment problem I'd much prefer direction or instruction on how to do this problem in general.