Unit 5 of 5
Study guide for CLEP CLEP Precalculus — Unit 5: Sequences, Series & Limits. Practice questions, key concepts, and exam tips.
39
Practice Questions
14
Flashcards
4
Key Topics
Try these 5 questions from this unit. Sign up for full access to all 39.
What is the limit of 1 / x as x approaches 0 from the left?
0
1
-1
-Infinity
Infinity
Answer: D — -Infinity is correct because as x approaches 0 from left, 1/x approaches -Infinity.
Find the value of the one-sided limit: lim x→0+ (x / |x|)
1
-1
0
undefined
1 and -1
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.
What is the horizontal asymptote of the rational function f(x) = as x increases without bound?
y = -1
y = 2
y = 1/2
y = 2/3
y = 0
Answer: E — Since the degree of the numerator is less than the degree of the denominator, the horizontal asymptote is y = 0.
Find the limit of 1 / as x approaches 3.
0
1/9
Infinity
-Infinity
The limit does not exist
Answer: C — Infinity is correct because as x approaches 3, the denominator approaches zero and is always positive, making the fraction larger.
What is the value of the limit as x approaches 2 of ?
4
2
0
undefined
-4
Answer: A — To 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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