3880544
Descripción
Test por Will Rickard, actualizado hace más de 1 año
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Creado por Will Rickard
hace alrededor de 9 años
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Pregunta 1
Pregunta
(a,b)
Respuesta
-
a ≤ x ≤ b
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{x ∈ R : a ≤ x ≤ b }
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{x ∈ R : a < x < b }
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a < x < b
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(4,1)
Pregunta 2
Pregunta
What are sets with curved brackets named?
Respuesta
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Open Intervals
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Closed Intervals
Pregunta 3
Pregunta
What are sets with square brackets named?
Respuesta
-
Closed Intervals
-
Open Intervals
Pregunta 4
Pregunta
State the triangle inequality
Respuesta
-
|a + b| ≤ |a| + |b|
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a + b ≤ |a| + |b|.
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|a + b| < |a| + |b|
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|a + b| ≤ |a| - |b|.
Pregunta 5
Pregunta
Define what is meant by a sequence
Respuesta
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Corresponds to a mapping (or ) from the natural numbers N to the real numbers R.
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Ordered list
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Numbers in a set
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corresponds to a mapping (or ) from a number to another
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corresponds to a mapping (or ) from the real numbers R to the real numbers N.
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Corresponds to a mapping (or ) from the natural numbers N to the integers Z.
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An increasing list of values mapped from the Natural numbers N to the integers Z
Pregunta 6
Pregunta
Define tends to infinity
Respuesta
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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.
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It gets bigger and bigger past a number
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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.
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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.
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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.
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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.
Pregunta 7
Pregunta
Define Tends to infinity
Respuesta
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∀A>0 ∃N∈N s.t. an>A ∀n>N
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∃A>0 ∃N∈N s.t. an>A ∀n>N
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∀A>0 ∀N∈N s.t. anN
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∀A>0 ∃N∈N s.t. an>A ∀n<N
Pregunta 8
Pregunta
What is |x|^2 equal to ?
Respuesta
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x^2
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x
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|x|
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-x
Pregunta 9
Pregunta
What's another way to write √(x^2)
Respuesta
-
|x|
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x
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x^2
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|x+1|
Pregunta 10
Pregunta
|xy| =
Respuesta
-
|x||y|
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xy
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|x+y|
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|x|+|y|
Pregunta 11
Pregunta
Define Convergent sequence
Respuesta
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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
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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
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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
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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
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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
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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
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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
Pregunta 12
Pregunta
(Converging series) If |an-l| = 1/n. What should you let N be greater than?
Respuesta
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1/e
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e
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2e
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2/e
Pregunta 13
Pregunta
Define bounded above
Respuesta
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if there exists some M ∈ R such that an ≤ M for all n ∈ N
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if there exists some M ∈ N such that an ≤ M for all n ∈ N
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if there exists some M ∈ R such that an ≤ R for all n ∈ N
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if there exists some M ∈ R such that an ≤ M for some n ∈ N
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if there exists some M ∈ R such that an ≤ M for all R ∈ N
Pregunta 14
Pregunta
Define bounded below
Respuesta
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there exists some M ∈ R such that an ≥ M for all n ∈ N.
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there exists some M ∈ R such that an < M for all n ∈ N.
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there exists some M ∈ N such that an < M for all n ∈ N.
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there exists some M ∈ N such that an ≥ M for all n ∈ N.
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there exists some M ∈ R such that an ≥ M for some n ∈ N.
Pregunta 15
Pregunta
Define bounded
Respuesta
-
there exist M1, M2 ∈ R such that M1 ≤ an ≤ M2 for all n ∈ N.
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there exist M1, M2 ∈ R such that M1 ≤ an ≤ M2 for some n ∈ N.
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there exist M1, M2 ∈ N such that M1 ≤ an ≤ M2 for all n ∈ N.
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there exist M1, M2 ∈ Q such that M1 ≤ an ≤ M2 for all n ∈ N.
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there exist M1, M2 ∈ R such that M1 < an < M2 for all n ∈ N.
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there exist M1, M2 ∈ R such that M1 ≤ an < M2 for all n ∈ N.
Pregunta 16
Pregunta
Give a sequence that is bounded but does not converge
an = [blank_start](-1)^n[blank_end]
Respuesta
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(-1)^n
Pregunta 17
Pregunta
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
Respuesta
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bounded
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convergent
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real
Pregunta 18
Pregunta
AOL: lim an = ℓ and lim bn = m
Then,
lim(an + bn) = ?
Respuesta
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ℓ + m,
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ℓm,
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ℓ - m
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ℓ + m - e
Pregunta 19
Pregunta
AOL: lim an = ℓ
Then,
lim λan = ?
Respuesta
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λℓ
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λ
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ℓ
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2λℓ
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λ+ℓ
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λ-ℓ
Pregunta 20
Pregunta
AOL: lim an = ℓ and lim bn = m
Then,
lim anbn = ?
Respuesta
-
ℓm
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ℓ/m
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ℓ + m
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ℓ - m
Pregunta 21
Pregunta
Sandwich Theorem/Squeeze Rule
Respuesta
-
. 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.
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. 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.
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. 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.
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. 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.
Pregunta 22
Pregunta
If |λ| < 1 then λ^n
n → ?
as n → ∞
Respuesta
-
0
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1
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n
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∞
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-∞
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2
-
λ
Pregunta 23
Pregunta
s>0
1/(n^s) → ?
as n → ∞.
Respuesta
-
0
-
∞
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n
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s
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1/s
Pregunta 24
Pregunta
(n^s)/ n! → ?
as n → ∞
Respuesta
-
0
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n
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n!
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∞
Pregunta 25
Pregunta
(λ^n)/n! → ?
as n → ∞.
Respuesta
-
λ
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n!
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0
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∞
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n
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