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Question #089de

1 Answer

Sep 3, 2016

# = 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#

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