0 < t <
+ −
< t < − −
< t < 3 − +
t > 3 + +
Since the velocity and acceleration have different signs over the intervals 0 < t < and < t
< 3, the correct answer is (B).
- A First, determine where f(x) and the x-axis intercept, i.e., solve f(x) = 0 for x. Thus, x = 0, x =
−2, and x = 2. In order to determine the area under the curve, we must set up and solve two
integrals: (4x^2 + x^4 ) dx + (4x^2 + x^4 ) dx = .
- C The line y = c is a horizontal asymptote of the graph of y = f(x) if the limit of the function as x
approaches positive and negative infinity equals c. Similarly, the line x = k is a vertical
asymptote of the graph of y = f(x) if the limit of the function as x approaches k from the left and
right is positive or negative infinity. First, check for a horizontal asymptote, so there is a
horizontal asymptote, = 3 and =3, so there is a horizontal asymptote at y
= 3. Next, check for a vertical asymptote; always check the point where the denominator is
undefined, in this case, x = −7: = ∞ and = − ∞. Thus, there is a
vertical asymptote at x = −7.
- D Use u-substitution in which u = x^2 − 7 and du = 2x dx. Thus, the integral is:
= ln|u| = In|x^2 − 7 | + C
- B The formula for the area between two curves is (f (x) − g (x)) dx, where a and b are the x-
coordinates that bind the region and f(x) is the more positive curve. Be careful to check if the
