Given (sqrt(x+1) - sqrt(2x+1)) / (sqrt(3x+4) - sqrt(2x+4) ] how do you find the limit as x approaches 0?
1 Answer
Change the way it is written to avoid
Explanation:
By the time this problem is assigned, I assume students have seen things like
In this problem, we have to try something, so late's use the same trick on both the numerator and denominator
= ((x+1-(2x+1))(sqrt(3x+4)+sqrt(2x+4)))/((x+4-4)(sqrt(x+1)+sqrt(2x+1)))
= (-x(sqrt(3x+4)+sqrt(2x+4)))/(x (sqrt(x+1)+sqrt(2x+1)))
= (-(sqrt(3x+4)+sqrt(2x+4)))/ (sqrt(x+1)+sqrt(2x+1)) " " (forx != 0 )
= -(sqrt4+sqrt4)/(sqrt1+sqrt1) = (-4)/2=-2
The same algebra with simplified notation gets us
= ((a-b)(sqrtc+sqrtd))/((c-d)(sqrta+sqrtb))