Velocity of a Motorcycle The distance s (in feet) covered by a
motorcycle traveling in a...
Velocity of a Motorcycle The distance s (in feet) covered by a
motorcycle traveling in a straight line and starting
from rest in t sec is given by the function
s(t) = −0.1t3 + 4t2 + 26t (0 ≤ t ≤ 3)
Calculate the motorcycle's average velocity (in ft/sec) over the
time interval [2, 2 + h] for h = 1, 0.1, 0.01, 0.001,
0.0001, and 0.00001. (Round your answers to four decimal
places.)
h = 1 ___________
h =...
Let f(x)=4+12x−x^3. Find (a) the intervals on which ff is
increasing, (b) the intervals on which...
Let f(x)=4+12x−x^3. Find (a) the intervals on which ff is
increasing, (b) the intervals on which ff is decreasing, (c) the
open intervals on which ff is concave up, (d) the open intervals on
which f is concave down, and (e) the x-coordinates of all
inflection points.
(a) f is increasing on the interval(s) =
(b) f is decreasing on the interval(s) =
(c) f is concave up on the open interval(s) =
(d) f is concave down on the...
1. Let S = {a, b, c}. Find a set T such that S ∈ T...
1. Let S = {a, b, c}. Find a set T such that S ∈ T and S ⊂
T.
2. Let A = {1, 2, ..., 10}. Give an example of two sets S and B
such that S ⊂ P(A), |S| = 4, B ∈ S and |B| = 2.
3. Let U = {1, 2, 3} be the universal set and let A = {1, 2}, B
= {2, 3} and C = {1, 3}. Determine the...
Let S = {0,2,4,6} and T = {1,3,5,7}. Determine
whether each of the following sets of...
Let S = {0,2,4,6} and T = {1,3,5,7}. Determine
whether each of the following sets of ordered pairs is a function
with domain S and codomain T. If so, is it
one-to-one? Is it onto?
a. {(0,2),(2,4),(4,6),(6,0)}
b. {(6,3),(2,1),(0,3),(4,5)}
c. {(2,3),(4,7),(0,1),(6,5)}
d. {(2,1),(4,5),(6,3)}
e. {(6,1),(0,3),(4,1),(0,7),(2,5)}
Let f (x) = 3x^4 −4x^3 −12x^2 + 1, defined on R.
(a) Find the intervals...
Let f (x) = 3x^4 −4x^3 −12x^2 + 1, defined on R.
(a) Find the intervals where f is increasing, and decreasing.
(b) Find the intervals where f is concave up, and concave
down.
(c) Find the local maxima, the local minima, and the points of
inflection.
(d) Find the Maximum and Minimum Absolute of f over [−2.3]
If a rock is thrown upward on the planet Mars with a velocity of
15 m/s,...
If a rock is thrown upward on the planet Mars with a velocity of
15 m/s, its height (in meters) after t seconds is given by H = 15t
− 1.86t^2
a) find the average velocity over the given time intervals: (i)
[2, 3] (ii) [2, 2.5] (iii) [2, 2.1] (iv) [2, 2.01] (v) [2,
2.001]
b) Estimate the instantaneous velocity when t=2.