Direct substitution is the name of the game, so we will directly substitute a -2 in for every x.
(-2)2 + 3(-2) + 1
Next, we can use our superior arithmetic skills to simplify our solution.
4 – 6 + 1 = -1
The limit, as x approaches -2, is -1. The limit, as we approach this problem, is very high, because it isn't too hard.
Example 2
Evaluate .
Is it Thanksgiving already? We won't complain; we'll take any excuse to plug in some pi.
Our trig skills are still sharp, so we know how to figure this out. For starters, sin(π) is 0. Secant tries to trick us up, but then we remember that it's cosine's reciprocal. That makes it easy to figure out that sec(π) must be -1.
sin (π) sec (π) = (0)(-1) = 0
Mmmm. We think we'll try a slice of blueberry next.
Example 3
Evaluate .
Even though we can see that (x – 2) can be simplified out, we're going to use direct substitution to solve this one. We should get the same answer either way.
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