one more, sorry!

[josh123]

Find [f(x + h) - f(x)]/h if f(x) = x + ln(2x)

a. 1 + (1/h){ln[(x + h)/x]}
b. 1 + (2/h){ln[(x + h)/x]}
c. 2 + (1/h){ln[(x + h)/x]}
d. 2 + (2/h){ln[(x + h)/x]}
e. (1/h)[1 + ln[(x + h)/x]
f. none of these

 

[stapel]

Don't do this all at one go; that rarely works. Instead, do this in pieces.

You have f(x), so no worries there.

Plug "x + h" in for "x" to find f(x + h).

Then subtract the former from the latter.

Simplify. See if you can factor an "h" out front. (You might or might not, but always check.)

Divide by h. Cancel off, if you can.

If you get stuck, please reply showing how far you have gotten. Thank you.

Eliz.

 

[josh123]

is this the answer? 2 + (2/h){ln[(x + h)/x]}

 

[stapel]

You caught the similification with the logs: good work there!

But I'm not sure where the 2's are coming from...?

Eliz.

 

[josh123]

1 + (1/h){ln[(x + h)/x]}

 

[stapel]

That's what I'm getting. Nice work.

Eliz.