How do you compute the rate of change of the function #f(x) = 1+1/(x+1)# at the point #x = a#?
1 Answer
Aug 3, 2017
Using the definition, see below.
Explanation:
The rate of change at
or
Using the second form, we have
# = lim_(xrarra)(1/(x+1) - 1/(a+1))/(x-a)#
# = lim_(xrarra)(((a+1)-(x+1))/((x+1)(a+1)))/((x-a)/1)#
# = lim_(xrarra)(a-x)/((x+1)(a+1)) * 1/(x-a)#
# = lim_(xrarra)(-1(cancel(x-a)))/((x+1)(a+1)) * 1/(1(cancel(x-a))#
# = (-1)/((a+1)(a+1)) = (-1)/(a+1)^2#