Unit 5 of 5

Unit 5: Sequences, Series & Limits

Study guide for CLEP CLEP PrecalculusUnit 5: Sequences, Series & Limits. Practice questions, key concepts, and exam tips.

39

Practice Questions

14

Flashcards

4

Key Topics

Key Concepts to Study

Arithmetic and geometric sequences
Series and summation notation
Intuitive concept of limits
Binomial theorem and counting principles

Sample Practice Questions

Try these 5 questions from this unit. Sign up for full access to all 39.

Q1MEDIUM

What is the limit of 1 / x as x approaches 0 from the left?

A.

0

B.

1

C.

-1

D.

-Infinity

E.

Infinity

Show Answer

Answer: D-Infinity is correct because as x approaches 0 from left, 1/x approaches -Infinity.

Q2MEDIUM

Find the value of the one-sided limit: lim x→0+ (x / |x|)

A.

1

B.

-1

C.

0

D.

undefined

E.

1 and -1

Show Answer

Answer: ATo evaluate the one-sided limit lim x→0+ (x / |x|), we consider x approaching 0 from the right, meaning x is positive. When x is positive, |x| equals x. So, the expression simplifies to x/x, which equals 1 for all x ≠ 0. Therefore, as x approaches 0 from the right, the limit is 1.

Q3MEDIUM

What is the horizontal asymptote of the rational function f(x) = 2x+1x2+3x+2\frac{2x + 1}{x^2 + 3x + 2} as x increases without bound?

A.

y = -1

B.

y = 2

C.

y = 1/2

D.

y = 2/3

E.

y = 0

Show Answer

Answer: ESince the degree of the numerator is less than the degree of the denominator, the horizontal asymptote is y = 0.

Q4HARD

Find the limit of 1 / (x3)2(x - 3)^{2} as x approaches 3.

A.

0

B.

1/9

C.

Infinity

D.

-Infinity

E.

The limit does not exist

Show Answer

Answer: CInfinity is correct because as x approaches 3, the denominator approaches zero and is always positive, making the fraction larger.

Q5MEDIUM

What is the value of the limit as x approaches 2 of x24x2\frac{x^2 - 4}{x - 2}?

A.

4

B.

2

C.

0

D.

undefined

E.

-4

Show Answer

Answer: ATo evaluate the limit as x approaches 2 of (x^2 - 4) / (x - 2), first factor the numerator to get ((x - 2)(x + 2)) / (x - 2). Then, cancel out the (x - 2) terms to get (x + 2). Now, substitute x = 2 into the simplified expression to get 2 + 2 = 4.

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Study Tips for Unit 5: Sequences, Series & Limits

  • Focus on understanding concepts, not memorizing facts — CLEP tests application
  • Practice with timed questions to build exam-day speed
  • Review explanations for wrong answers — they reveal common misconceptions
  • Use flashcards for key terms, practice questions for deeper understanding

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