How do you use the limit definition to find the slope of the tangent line to the graph #f(x)=sqrt(x)# at x=4?
1 Answer
Oct 16, 2016
Details depend on exactly which limit definition of the slope of the tangent line you are using.
Explanation:
# = lim_(trarr4)((sqrtt-sqrt4))/((t-4))* ((sqrtt+sqrt4))/ ((sqrtt+sqrt4))#
# = lim_(trarr4)(t-4)/((t-4)(sqrtt+sqrt4))#
# = lim_(trarr4) 1/ (sqrtt+sqrt4)#
# = 1/(sqrt4 + sqrt4) = 1/(2+2) = 1/4#
