Question

How can I go about solving this problem:
lim (sqrt(x)-x^2)/(1-sqrt(x)) as x approaches 1?

Answer 1

Use L'Hopital's Rule
It then changes to (1/2x^-1/2 - 2x)/(-1/2x^-1/2) = (1/2-2)/-1/2 = 3

Answer 2

Since it is of the type 0/0 we can use L'hospital rule
\(\lim_{x\to 1}\frac{\frac{1}{2\sqrt{x}}-2x}{-\frac{1}{2\sqrt{x}}}=\frac{\frac{1}{2}-2}{-\frac{1}{2}}=3\)

Answer 3

Thank you for your assistance. I understand the process and the incorrect procedure that I committed.