Question

Pre-calc - image attached

Answer 1

Explanation:

We see that if we do a direct substitution for x as 1 we have a 0 in the denominator, which is a big no-no. So we try to manipulate the function so that doesn't happen. We can factor the numerator. When we do that we get

`\lim_(x \to 1) ((x-1)(x^2+x+1))/((x-1))` The (x-1) terms cancel out leaving us with just

`\lim_(x \to 1) (x^2+x+1)` which is no longer a problem! This limit is found by subbing in a 1 for x and doing the math. The limit is 3.