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Unit 5: Sequences, Series & Limits

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

48

Practice Questions

11

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 48.

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: A — To 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.

Q3EASY

Determine the limit of 1/x as x approaches infinity.

A) 0
B) 1
C) -1
D) 2
E) Does not exist
Show Answer

Answer: A — 0 is correct because as x increases, 1/x approaches 0.

Q4MEDIUM

What is the horizontal asymptote of the rational function f(x) = (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: E — Since the degree of the numerator is less than the degree of the denominator, the horizontal asymptote is y = 0.

Q5HARD

Find the limit of 1 / (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: C — Infinity is correct because as x approaches 3, the denominator approaches zero and is always positive, making the fraction larger.

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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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