Question

You are given a function f : [4, 8] → [-3, -2] and the partition P = {4,5,7,8} of the interval [4, 8]. Which of the following are true and which are false?

U(f,P) > 0

U(f,P) < L(f,P)

L(f,P) ≤ 0

U(f,P) ≤ -8

Answer #1

I use the definition of UPF and LPF to solve this problem

Consider the function f(x)=1/x on the interval [1,2]. Let P be a
uniform partition of [1,2] with 8 sub-intervals. Compute the left
and right Riemann sum of ff on the partition. Enter approximate
values, rounded to three decimal places.

Let
f(x) =
x
0 ≤ x ≤ 1/2
= 3 -
x 1/2 < x ≤
1
Find a partition P of [0,1] such that U(f, P) - L(f, P) <
1/100

The translational partition function of a molecule is given
by:
qT=(2 π m k T)3/2 (V/h3).
(Note: m in the equation is the mass of the individual
molecule).
If V=1 L and T=300 K answer the following question:
a) qT for HI at T = 300 K, and V = 1 L.
b) qT for HI at T = 2000 K, and V = 1 L.

Given p(x) = ? 3(?+4) 3 on [0, ∞), Find the constant C such that
p(x) is a probability density function on the given interval and
compute ?(0 ≤ ? ≤ 1).

Given that a function F is differentiable.
a
f(a)
f1(a)
0
0
2
1
2
4
2
0
4
Find 'a' such that limx-->a(f(x)/2(x−a)) = 2.
Provide with hypothesis and any results used.

1. Decide if f(x) = 1/2x2dx on the interval [1, 4] is
a probability density function
2. Decide if f(x) = 1/81x3dx on the interval [0, 3]
is a probability density function.
3. Find a value for k such that f(x) = kx on the interval [2, 3]
is a probability density function.
4. Let f(x) = 1 /2 e -x/2 on the interval [0, ∞).
a. Show that f(x) is a probability density function
b. . Find P(0 ≤...

1. f is a probability density function for the random
variable X defined on the given interval. Find the
indicated probabilities.
f(x) = 1/36(9 − x2); [−3, 3]
(a) P(−1 ≤ X ≤ 1)(9 −
x2); [−3, 3]
(b) P(X ≤ 0)
(c) P(X > −1)
(d) P(X = 0)
2. Find the value of the constant k such that the
function is a probability density function on the indicated
interval.
f(x) = kx2; [0,
3]
k=

Suppose that the pdf for X is f ( x ) = 3 8 x 2 , 0 ≤ x ≤ 2,
f(x) = 0 otherwise. Suppose that Y is uniformly distributed on the
interval from x to 2x for any given x.
Determine P(Y < 2)

find the interval where the function is increasing and
decreasing f(x) =(x-8)^2/3
a) decreasing (8, infinity) increasing (-infinity, 8) local max
f(8)=0
a) decreasing (- infinity, 8) increasing (8, infinity) local max
f(8)=0
a) decreasing (-infinity, infinity) no extrema
a) increasing (-infinity, infinitely) no extrema

Find the particular antiderivative that satisfies the following
conditions:
A) p'(x)=-20/X^2 ; p(4)=3
B) p'(x)=2x^2-7x ; p(0)=3,000
C) Consider the function f(x)=3cosx−7sinx.
Let F(x) be the antiderivative of f(x) with F(0)=7
D) A particle is moving as given by the data:
v(t)=4sin(t)-7cos(t) ; s(0)=0

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