Question

How do you find the derivative of `h(s)=3+2/3s` using the limit process?

Answer 1

`(dh(s))/(ds) =2/3`
...see below for solution using limit process

Explanation:

`(dh(s))/(ds) = lim_(krarr0) (color(red)(h(s+k))-color(blue)(h(s)))/k`

`color(white)("XXX")=lim_(krarr0)((color(red)(3+2/3(s+k)))-(color(blue)(3+2/3s)))/k`

`color(white)("XXX")=lim_(krarr0)(2/3cancel(k))/cancel(k)`

`color(white)("XXX")=lim_(krarr0)2/3`

`color(white)("XXX")=2/3`