Question

If the limit as x approaches 1 for (f(x) - 7)/(x-1)=8,
evaluate the limit as x approaches 1 for f(x)

Answer 1

the left is undefined as x >> 1
but for any other x very close to x = 1
f(x) - 7 = 8(x-1)
for example if x = .99
f(.99) - 7 = 8(.99-1) = 8 (-.01) = - .08
f(.99) = 7 -.08
which might give us a hint as to where f(x) was going :)
in fact it looks to me like
f(x) - 7 = 8(x-1)
is similar to
f(x) = 7 + 8(x-1)
and as x >>1
f(1) =7 +8(0) = 7

Answer 2

Thank you so much!!