Question

Please help. This is summer work for AP Calc. SIMPLIFY ** (1/x+h) - (1/x) **

Answer 1

this for finding derivative of 1/x using limits right?

\[\lim_{h \rightarrow 0} \frac{\frac{1}{x+h} - \frac{1}{x}}{h}\]

Answer 2

combine fractions using common denominator "x(x+h)"
\[\rightarrow \frac{x - (x+h)}{x (x+h)}\]

Answer 3

Oh. Thank you!

Answer 4

no problem :)

Answer 5

Wait. Would that be the simplest form? Or would any terms cancel out?

Answer 6

you tell me ... what happens when you distribute the negative and add

x-(x+h) = x -x -h

Answer 7

It would be (-h) / x(x+h).. Right?

Answer 8

yep

Answer 9

Thank you so much