How to solve #lim_(x->0)((1/(x(sqrt(x+1))))-1/x)#?
1 Answer
Dec 28, 2017
Please see below.
Explanation:
Get a single quotient, then rationalize the numerator.
# = ((1-sqrt(x+1)))/(xsqrt(x+1)) * ((1+sqrt(x+1)))/ ((1+sqrt(x+1)))#
# = (1-x-1)/(xsqrt(x+1)(1+sqrt(x+1)))#
# = (-1)/(sqrt(x+1)(1+sqrt(x+1)))#
# = (-1)/(sqrt1(1+sqrt1)) = -1/2#
We don't need it but here is the graph:
graph{1/(xsqrt(x+1))-1/x [-3.33, 6.537, -3.61, 1.322]}