1. The problem statement, all variables and given/known data Evaluate lim y→4 y-3√y + 2 √y - 2 3. The attempt at a solution If I plug 4 into Y, my answer is undefined. But if I do the chart method, where I plug in 3.999 and 4.0001 the answer is 1. So I'm not quite sure what I'm doing wrong.
Try factoring the numerator! The square roots might throw you off a bit, but it's in the same form of a quadratic equation. You can't plug in 4 directly because the function isn't defined at 4. But limits don't concern themselves with what happens at that point, only what happens very close to that point.
The numerator is quadratic in form, and can be factored. Or, you can let u = √y, and rewrite the fraction in terms of u, and factor the numerator. With this change, the limit will be as u → 2.
Mark and Scurty, thank you. Mark I get your second method, but for both of you, I don't understand how to factor the numerator. Is it really factor-able? I dont get what value to factor by.