Question

Suppose R>0. Which of the following statements might be true about a power series centered about the point x=a

a) The series converges for all x>a

b) The series converges on the interval (a,R)

c)The series converges on the interval [a,R)

d) The series converges only at x=a+R

e) All of the above

f) None of the above

Answer #1

The power series centered about the point **x = a**
satisfies exactly one of the below properties.

1- The series converges for all real numbers.

2- The series converges at **x = a** and diverges
for all other real numbers.

3- There exists a real number **R > 0** such
that for **|x - a| < R**, the series converges and
for **|x - a| > R**, the series diverges. The
series may converge or diverge at **x = a - R** and
**x = a + R**.

Hence, for **R > 0**, the only statement that
might be true about a power series centered about the point
**x = a** is

f) None of the above

Suppose R>0. Which of the following statements might be true
about a power series centered about the point x=a
a) The series converges for all x>a
b) The series converges on the interval (a,R)
c)The series converges on the interval [a,R)
d) The series converges only at x=a+R
e) All of the above
f) None of the above

Let f have a power series representation, S. Suppose that
f(0)=1, f’(0)=3, f’’(0)=2 and f’’’(0)=5.
a. If the above is the only information we have, to what degree
of accuracy can we estimate f(1)?
b. If, in addition to the above information, we know that S
converges on the interval [-2,2] and that |f’’’’(x)|< 11 on that
interval, then to what degree of accuracy can we estimate
f(1)?

Which of the following statements is true?
a) The geometric series Σ∞n=1 r^n is always convergent.
b) for the series Σ∞n=1an, if lim n→∞ an = 1/3, then the series
will be convergent.
c) If an> bn for all values of n and Σ∞n=1 bn is convergent,
then Σ∞ n=1an is also convergent.
d) None of the above

Find the power series expansion for f(x) = x^2 e^(x^2) centered
at a = 0 and centered at a=-3

Suppose the power series for a function f(x) has the interval of
convergence I=(a,b]. Which of the following statement must be true
about the interval of convergence for the power series \int
f(x)dx?
I=[a,b)
I=(a,b)
I=(a,b]
I=[a,b]
Can't be determined.

Question 10 (1 point)
Which of the following statements is true?
a
Purchasing power is the ability to buy goods and services.
b
While goods are tangible (say, apples and laptops), services are
intangible (say, haircuts and lawn mowing).
c
Income is the amount of money one makes a year.
d
All of the above.
e
Only a) and b)
Question 11 (1 point)
Which of the following statements is true?
a
Price is the amount of money that must...

Use a power series centered about the ordinary point x0 = 0 to
solve the differential equation
(x − 4)y′′ − y′ + 12xy = 0
Find the recurrence relation and at least the first four nonzero
terms of each of the two linearly inde-
pendent solutions (unless the series terminates sooner).
What is the guaranteed radius of
convergence?

Which of the following statements is true? a. Physicians might
not induce demand because they would lose leisure time. b. the
concept of perfect agency is realistic. c. Information asymmetry is
not necessary for physician demand inducement. d. All of the above.
e. A & B only.

find the power series representation centered at a=0 of
a.) f(x) = x/(5+7x)
b.) f(x) = x^2 sin(3x)

Which of the following is true about the graph of
f(x)=8x^2+(2/x)−4?
a) f(x) is increasing on the interval
(−∞,0).
b) f(x) has a vertical asymptote at
x=2.
c) f(x) is concave down on the interval
(0,∞).
d) f(x) has a point of inflection at the point
(0,−4).
e) f(x) has a local minimum at the point
(0.50,2).
Suppose
f(x)=12xe^(−2x^2)
Find any inflection points.

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