3880544
Descrição
Quiz por Will Rickard, atualizado more than 1 year ago
|
Criado por Will Rickard
aproximadamente 9 anos atrás
|
|
Questão 1
Questão
(a,b)
Responda
-
a ≤ x ≤ b
-
{x ∈ R : a ≤ x ≤ b }
-
{x ∈ R : a < x < b }
-
a < x < b
-
(4,1)
Questão 2
Questão
What are sets with curved brackets named?
Responda
-
Open Intervals
-
Closed Intervals
Questão 3
Questão
What are sets with square brackets named?
Responda
-
Closed Intervals
-
Open Intervals
Questão 4
Questão
State the triangle inequality
Responda
-
|a + b| ≤ |a| + |b|
-
a + b ≤ |a| + |b|.
-
|a + b| < |a| + |b|
-
|a + b| ≤ |a| - |b|.
Questão 5
Questão
Define what is meant by a sequence
Responda
-
Corresponds to a mapping (or ) from the natural numbers N to the real numbers R.
-
Ordered list
-
Numbers in a set
-
corresponds to a mapping (or ) from a number to another
-
corresponds to a mapping (or ) from the real numbers R to the real numbers N.
-
Corresponds to a mapping (or ) from the natural numbers N to the integers Z.
-
An increasing list of values mapped from the Natural numbers N to the integers Z
Questão 6
Questão
Define tends to infinity
Responda
-
A sequence (an) of real numbers tends to infinity if given any real number A > 0 there exists N ∈ N such that an>A for all n>N.
-
It gets bigger and bigger past a number
-
A sequence (an) of numbers tends to infinity if given any number A > 0 there exists N ∈ N such that an>A for all n>N.
-
A sequence (an) of real numbers goes to infinity if given any real number A > 0 there exists N ∈ N such that an>A for all A>N.
-
A sequence (an) of real numbers tends to infinity if given any real number A > 0 there exists N ∈ N such that an>A for some A>N.
-
A sequence (an) of real numbers tends to infinity if given any real number A > 0 there exists z ∈ Z such that an>A for all A>N.
Questão 7
Questão
Define Tends to infinity
Responda
-
∀A>0 ∃N∈N s.t. an>A ∀n>N
-
∃A>0 ∃N∈N s.t. an>A ∀n>N
-
∀A>0 ∀N∈N s.t. anN
-
∀A>0 ∃N∈N s.t. an>A ∀n<N
Questão 8
Questão
What is |x|^2 equal to ?
Responda
-
x^2
-
x
-
|x|
-
-x
Questão 9
Questão
What's another way to write √(x^2)
Responda
-
|x|
-
x
-
x^2
-
|x+1|
Questão 10
Questão
|xy| =
Responda
-
|x||y|
-
xy
-
|x+y|
-
|x|+|y|
Questão 11
Questão
Define Convergent sequence
Responda
-
A sequence (an) of real numbers converges to a real number ℓ if given any e > 0 there exists N ∈ N such that |an − ℓ| < e for all n > N
-
A sequence (an) of numbers converges to a real number ℓ if given any e > 0 there exists N ∈ N such that |an − ℓ| < e for all n > N
-
A sequence (an) of real numbers converges to a number ℓ if given any e > 0 there exists N ∈ N such that |an − ℓ| < e for all n > N
-
A sequence (an) of real numbers converges to a real number ℓ if given any e < 0 there exists N ∈ N such that |an − ℓ| < e for all n > N
-
A sequence (an) of real numbers converges to a real number ℓ if given any e > 0 there exists Z ∈ N such that |an − ℓ| < e for all n > N
-
A sequence (an) of real numbers converges to a real number ℓ if given any e > 0 there exists N ∈ N such that |an − ℓ| < e for some n > N
-
A sequence (an) of real numbers converges to a real number ℓ if given any e > 0 there exists N ∈ N such that |e − ℓ| < e for all n > N
Questão 12
Questão
(Converging series) If |an-l| = 1/n. What should you let N be greater than?
Responda
-
1/e
-
e
-
2e
-
2/e
Questão 13
Questão
Define bounded above
Responda
-
if there exists some M ∈ R such that an ≤ M for all n ∈ N
-
if there exists some M ∈ N such that an ≤ M for all n ∈ N
-
if there exists some M ∈ R such that an ≤ R for all n ∈ N
-
if there exists some M ∈ R such that an ≤ M for some n ∈ N
-
if there exists some M ∈ R such that an ≤ M for all R ∈ N
Questão 14
Questão
Define bounded below
Responda
-
there exists some M ∈ R such that an ≥ M for all n ∈ N.
-
there exists some M ∈ R such that an < M for all n ∈ N.
-
there exists some M ∈ N such that an < M for all n ∈ N.
-
there exists some M ∈ N such that an ≥ M for all n ∈ N.
-
there exists some M ∈ R such that an ≥ M for some n ∈ N.
Questão 15
Questão
Define bounded
Responda
-
there exist M1, M2 ∈ R such that M1 ≤ an ≤ M2 for all n ∈ N.
-
there exist M1, M2 ∈ R such that M1 ≤ an ≤ M2 for some n ∈ N.
-
there exist M1, M2 ∈ N such that M1 ≤ an ≤ M2 for all n ∈ N.
-
there exist M1, M2 ∈ Q such that M1 ≤ an ≤ M2 for all n ∈ N.
-
there exist M1, M2 ∈ R such that M1 < an < M2 for all n ∈ N.
-
there exist M1, M2 ∈ R such that M1 ≤ an < M2 for all n ∈ N.
Questão 16
Questão
Give a sequence that is bounded but does not converge
an = [blank_start](-1)^n[blank_end]
Responda
-
(-1)^n
Questão 17
Questão
Lemma 1.9, Convergent sequences are bounded. Every [blank_start]convergent[blank_end] sequence of [blank_start]real[blank_end] numbers is a [blank_start]bounded[blank_end] sequence
Responda
-
bounded
-
convergent
-
real
Questão 18
Questão
AOL: lim an = ℓ and lim bn = m
Then,
lim(an + bn) = ?
Responda
-
ℓ + m,
-
ℓm,
-
ℓ - m
-
ℓ + m - e
Questão 19
Questão
AOL: lim an = ℓ
Then,
lim λan = ?
Responda
-
λℓ
-
λ
-
ℓ
-
2λℓ
-
λ+ℓ
-
λ-ℓ
Questão 20
Questão
AOL: lim an = ℓ and lim bn = m
Then,
lim anbn = ?
Responda
-
ℓm
-
ℓ/m
-
ℓ + m
-
ℓ - m
Questão 21
Questão
Sandwich Theorem/Squeeze Rule
Responda
-
. Let N ∈ N and ℓ ∈ R. Suppose (an), (bn) and (cn) are sequences satisfying an ≤ bn ≤ cn for all n ≥ N. If an → ℓ and cn → ℓ, then bn → ℓ.
-
. Let N ∈ N and ℓ ∈ R. Suppose (an), (bn) and (cn) are sequences satisfying an ≤ n ≤ cn for all n ≥ N. If an → ℓ and cn → ℓ, then bn → ℓ.
-
. Let N ∈ R and ℓ ∈ N. Suppose (an), (bn) and (cn) are sequences satisfying an ≤ bn ≤ cn for all n ≥ N. If an → ℓ and cn → ℓ, then bn → ℓ.
-
. Let N ∈ N and ℓ ∈ R. Suppose (an), (bn) and (cn) are sequences satisfying an ≤ bn ≤ cn for some n ≥ N. If an → ℓ and cn → ℓ, then bn → ℓ.
Questão 22
Questão
If |λ| < 1 then λ^n
n → ?
as n → ∞
Responda
-
0
-
1
-
n
-
∞
-
-∞
-
2
-
λ
Questão 23
Questão
s>0
1/(n^s) → ?
as n → ∞.
Responda
-
0
-
∞
-
n
-
s
-
1/s
Questão 24
Questão
(n^s)/ n! → ?
as n → ∞
Responda
-
0
-
n
-
n!
-
∞
Questão 25
Questão
(λ^n)/n! → ?
as n → ∞.
Responda
-
λ
-
n!
-
0
-
∞
-
n
Quer criar seus próprios Quizzes gratuitos com a GoConqr? Saiba mais.