Question

Question #089de

Answer 1

`= 1/14`

Explanation:

`lim_(h to 0) {sqrt(49 + h) - 7}/h`

`= lim_(h to 0) {7sqrt(1 + h/49) - 7}/h`

Binomial Expansion of sqrt term
`= lim_(h to 0) {7(1 + 1/2 h/49 + O(h^2)) - 7}/h`

`= lim_(h to 0) { 7/2h/49 + O(h^2) }/h`

`= lim_(h to 0) 1/14 + O(h)`

`= 1/14`