Limit

Question

Puzzle

$\lim_{y\rightarrow \alpha }\left (y-\left ( y^{2}+y \right )^{\frac{1}{2}}\right )$

Answer 1

Answer  = $- \frac{1}{2}$

It's an $∞ - ∞$ indeterminate form. Hence, We first convert it into $ \frac{0}{0}$ form and then apply D'Hopital's rule.

To convert it into $ \frac{0}{0}$ form... Take $y^2$ out of the Square root expression and then $y$ out from the whole expression. 

Comments

Or we can solve like this,