Question

Find the least upper bound and the greatest lower bound for the two polynomials:

a) p(x) = x^{4} - 3x^{2} - 2x + 5

b) p(x) = -2x^{5} + 5x^{4} + x^{3} - 3x
+ 4

Answer #1

f(x) =+x3−3x2+ 9x+ 13. Find an upper and a lower bound on the
real zeros of(x).

Find the greatest common divisor of the given polynomials over
the given field. Then write the greatest common
divisor as a linear combination of the given polynomials. That is,
given f(x) and g(x), find a(x) and b(x) so that d(x) = a(x)f(x) +
b(x)g(x), where d(x) is the greatest common divisor of f(x) and
g(x).
(a) x^10 − x^7 − x^5 + x^3 + x^2 − 1 and x^8 − x^5 − x^3 + 1
over Q.
(b) x^5 +...

1. y=∫upper bound is sqrt(x) lower bound is 1,
cos(2t)/t^9 dt
using the appropriate form of the Fundamental Theorem of
Calculus.
y′ =
2. Use part I of the Fundamental Theorem of Calculus to find the
derivative of
F(x)=∫upper bound is 5 lower bound is
x, tan(t^4)dt
F′(x) =
3. If h(x)=∫upper bound is 3/x and lower
bound is 2, 9arctan t dt , then
h′(x)=
4. Consider the function f(x) = {x if x<1, 1/x if x is >_...

Given the data listed in the table below, calculate the lower
and upper bound of the 90% prediction interval for the response
variable at X = 5. The regression equation is given by y^ =
b0 + b1x.
Regression Statistics
Statistic
Value
b0
9.6
b1
0.29
x
7.77
se
2.209
SSX
58.71
SST
34.98
n
40
Give your answer to 2 decimal places. You may find this
Student's t distribution table useful.
a) Lower bound =
b)Upper bound =

A random variable X follows the continuous uniform distribution
with a lower bound of −7 and an upper bound of 10. a. What is the
height of the density function f(x)? (Round your answer to 4
decimal places.) b. What are the mean and the standard deviation
for the distribution? (Round your answers to 2 decimal places.) c.
Calculate P(X ≤ −5). (Round intermediate calculations to at least 4
decimal places and final answer to 4 decimal places.)

find the upper bound of the LTE (euler)
2x'+2/3 x = 4x^2
and the interval for t is [0,1].

Given the data listed in the table below, calculate the lower
and upper bound of the 99% prediction interval for the response
variable at X = 3. The regression equation is given by y^ =
b0 + b1x.
Regression Statistics
Statistic
Value
b0
4.6
b1
1.15
x
4.81
se
1.772
SSX
52.29
SST
42.33
n
40
Give your answer to 2 decimal places. You may find this
Student's t distribution table useful.
a) Lower bound =
b)Upper bound =

Find the upper and lower sum of f(x) = 3x^2+4 on the interval
[0,2] with 4 equal subintervals.

let p(x) and Q(x) be two polynomials and consider the following
two cases:
case1:p(x) x Q(x)
case2: 3 Q (x)
for each case, find the following:
a) the number of terms
b) the degree

find greatest common divisor of x^5 + x^4 +1 and x^5+x+1, viewed
as elements in the ring F2[x] of polynomials over the finite field
F2 with 2 elements

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