Question

Evaluate

lim h->0 [f(1+h)−f(1)]/h

where f(x)=5x+7

and could you explain throughly how you did it?

Answer 1

5.

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.