Answer:
5.
Step-by-step explanation:
I think you mean:
lim h->0 [f(x+h)−f(x)]/h
If f(x) = 5x + 7, then f(x + h) = 5(x + h) + 7.
So:
lim h -->0 [5(x+h) + 7 - (5x + 7) ] / h
= lim h --->0 ( 5x + 5h + 7 - 5x - 7) / h
= lim h --->0 ( 5h) / h
The h's cancel, so:
lim h --> 0 is 5.
