Answer:
Step-by-step explanation:
The function has a horizontal asymptote which is
The function has a horizontal asymptote which is
The function has no horizontal asymptote because the numerator has a degree which is higher than the degree of the denominator,
The function has a horizontal asymptote which is
Answer:
x = -1, x = 1
Step-by-step explanation:
Factor the equation. (It's a difference of squares, so we know the form will be (a-b)(a+b).)
Test this by FOILing it out, if you're unsure. This is something it can be good to memorize!
Set it equal to 0.
Separate the two parenthetical expressions by the Zero Product Property.
Solve for x!
a. Use the mean value theorem. 16 falls between 12 and 20, so
(Don't forget your units - 5 m/min^2)
b. gives the Johanna's velocity at time
. The magnitude of her velocity, or speed, is
. Integrating this would tell us the total distance she has traveled whilst jogging.
The Riemann sum approximates the integral as
If you're not sure how this is derived: we're given 5 sample points, so we can cut the interval [0, 40] into 4 subintervals. The lengths of each subinterval are 12, 8, 4, and 16 (the distances between each sample point), and the height of the rectangle approximating the area under the plot of is determined by the value of
at each sample point, 200, 240, |-220| = 220, and 150.
c. Bob's velocity is given by , so his acceleration is given by
. We have
and at his acceleration is
m/min^2.
d. Bob's average velocity over [0, 10] is given by the difference quotient,
m/min