Evaluate

lim h->0 [f (1+h) - f (1) ]/h

where f (x) = 5x+7

and could you explain throughly how you did it?

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.