solve :

Question

lim [((2x+1)^0.5)-3]/[x-4]
x-->4

Answer 1

Multiply top and bottom by √(2x+1) + 3
and multiply the top out

so
= lim (2x+1 - 9)[(x-4)(√(2x+1) + 3)
x--->4

= lim 2/(√(2x+1) + 3)
x --->4

= 2/6
= 1/3