4 (1) − 6 = 4(1)^3 + 6(1)^2 − 2
−2 = 8
= −4
- C If we take the limit as x goes to from the left, we get an indeterminate form , so let’s use
L’Hôpital’s Rule. We take the derivative of the numerator and the denominator and we get = = . We can simplify this using trig identities: =. Now, when we take the limit we get. 2 sin x = 2.
23. B Using u-substitution, .
24. C Because the region is bound by three curves given in the form y = and x =, it is likely better to
use the cylindrical shells method to solve this problem: = .- D Follow the First Fundamental Theorem of Calculus: = = 64.
- C In order for f (x) to be continuous at a point c, there are three conditions that need to be
fulfilled.
(1) f(c) exists.(2) f(x) exists.(3) f(x) = f(c).First, let’s check condition (1): f (4) exists; it’s equal to k.Next, let’s check condition (2).