ANSWERS AND EXPLANATIONS TO SECTION I
- A First, use implicit differentiation to find :
x^2 + 2xy = 0
Isolate and simplify:
Next, take the second derivative via implicit differentiation:
Plug in and simplify:
- C When y = ln u, = . For this problem, u = 6x^3 − 2x^2 and = 18x^2 − 4x. Then, =
.
- D When you insert ∞ for x, the limit is , which is indeterminate. First, rewrite the limit as
. Then, use L’Hôpital’s Rule to evaluate the limit: . This limit exists and equals
0.
- C In order to approximate the error in the volume of the sphere use the approximation formula: dy
