isolate . Now, we take the derivative again: = . Next, because = 1 and , we get =
. This can be simplified to = .
8. 1
We can easily isolate y in this equation: y = x^2 − 2x + 1. We take the derivative: = x − 2.And we take the derivative again: = 1. Note that just because a problem has the x’s andy’s mixed together doesn’t mean that we need to use implicit differentiation to solve it!SOLUTIONS TO UNIT 1 DRILL
- π^2
To find the limit, we would plug in π for x, but there is no x in the limit. So the limit is simply
π^2.Here we are finding the limit as x goes to infinity. We divide the top and bottom by the highestpower of x in the expression: = . Next, simplify the topand bottom: . Now, if we take the limit as x goes to infinity, we get = = 0.
3.
Here we are finding the limit as x goes to infinity. We divide the top and bottom by the highestpower of x in the expression, which is x^2 . Notice that, under the radical, we divide by x^4