Evaluate the limit as x approaches 1 of the quotient of the square root of the quantity x squared plus 24 minus 5 and the quantity x minus 1.
sqr root(x^2 + 24) - 5
lim as x-> 1
x - 1
can you explain how i would prove this?

Ok, so if you tried to evaluate it, we would get something/0, which is undefined
not helpful

hmm
the next step would be to try and factor something out
well, I don't see what to factor out
the next try would be to use l'hopital's rule

take derivitive of top and bottom
derivitive of top is
derivitive of bottom is 1
so we get
if we input 1 for x we get
 
===
we know it can't be because if we evaluated it at x=0 and x=2, we see that it is above 0

the as x->1, =1/5