Estimate a limit from a table of values
12th grade (Year 13 in England) · 16 questions · Common Core: HSF.IF.A.2 · England: A-level Pure Mathematics
Name
Date
Score/ 16
Question 1
g(x) = (x³ − 1)/(x − 1). x: 0.9 | 0.99 | 0.999 | 1.001 | 1.01 | 1.1 g(x): 2.71 | 2.9701 | 2.997 | 3.003 | 3.0301 | 3.31 Estimate lim(x→1) g(x).
Answer
Question 2
x: 0.9 | 0.99 | 0.999 | 1.001 | 1.01 | 1.1 f(x): 1.9 | 1.99 | 1.999 | 2.001 | 2.01 | 2.1 Does lim(x→1) f(x) exist?
- A. Yes
- B. No: the two sides approach different values
Question 3
f(x) = (x² − 9)/(x + 3). It has no value at x = −3 itself. x: −3.1 | −3.01 | −3.001 | −2.999 | −2.99 | −2.9 f(x): −6.1 | −6.01 | −6.001 | −5.999 | −5.99 | −5.9 Estimate lim(x→−3) f(x).
Answer
Question 4
g(x) = (x³ + 27)/(x + 3). x: −3.1 | −3.01 | −3.001 | −2.999 | −2.99 | −2.9 g(x): 27.91 | 27.0901 | 27.009 | 26.991 | 26.9101 | 26.11 Estimate lim(x→−3) g(x).
Answer
Question 5
x: 0.9 | 0.99 | 0.999 | 1.001 | 1.01 | 1.1 f(x): −1 | −1 | −1 | 1 | 1 | 1 Does lim(x→1) f(x) exist?
- A. Yes
- B. No: the two sides approach different values
Question 6
f(x) = (x² − 4)/(x + 2). It has no value at x = −2 itself. x: −2.1 | −2.01 | −2.001 | −1.999 | −1.99 | −1.9 f(x): −4.1 | −4.01 | −4.001 | −3.999 | −3.99 | −3.9 Estimate lim(x→−2) f(x).
Answer
Question 7
g(x) = (x³ − 8)/(x − 2). x: 1.9 | 1.99 | 1.999 | 2.001 | 2.01 | 2.1 g(x): 11.41 | 11.9401 | 11.994 | 12.006 | 12.0601 | 12.61 Estimate lim(x→2) g(x).
Answer
Question 8
x: 2.9 | 2.99 | 2.999 | 3.001 | 3.01 | 3.1 f(x): −1 | −1 | −1 | 1 | 1 | 1 Does lim(x→3) f(x) exist?
- A. Yes
- B. No: the two sides approach different values
Question 9
f(x) = (x² − 9)/(x − 3). It has no value at x = 3 itself. x: 2.9 | 2.99 | 2.999 | 3.001 | 3.01 | 3.1 f(x): 5.9 | 5.99 | 5.999 | 6.001 | 6.01 | 6.1 Estimate lim(x→3) f(x).
Answer
Question 10
g(x) = (x³ + 8)/(x + 2). x: −2.1 | −2.01 | −2.001 | −1.999 | −1.99 | −1.9 g(x): 12.61 | 12.0601 | 12.006 | 11.994 | 11.9401 | 11.41 Estimate lim(x→−2) g(x).
Answer
Question 11
x: −3.1 | −3.01 | −3.001 | −2.999 | −2.99 | −2.9 f(x): −6.1 | −6.01 | −6.001 | −5.999 | −5.99 | −5.9 Does lim(x→−3) f(x) exist?
- A. Yes
- B. No: the two sides approach different values
Question 12
f(x) = (x² − 1)/(x + 1). It has no value at x = −1 itself. x: −1.1 | −1.01 | −1.001 | −0.999 | −0.99 | −0.9 f(x): −2.1 | −2.01 | −2.001 | −1.999 | −1.99 | −1.9 Estimate lim(x→−1) f(x).
Answer
Question 13
g(x) = (x³ + 1)/(x + 1). x: −1.1 | −1.01 | −1.001 | −0.999 | −0.99 | −0.9 g(x): 3.31 | 3.0301 | 3.003 | 2.997 | 2.9701 | 2.71 Estimate lim(x→−1) g(x).
Answer
Question 14
x: 0.9 | 0.99 | 0.999 | 1.001 | 1.01 | 1.1 f(x): −1 | −1 | −1 | 1 | 1 | 1 Does lim(x→1) f(x) exist?
- A. Yes
- B. No: the two sides approach different values
Question 15
f(x) = (x² − 25)/(x + 5). It has no value at x = −5 itself. x: −5.1 | −5.01 | −5.001 | −4.999 | −4.99 | −4.9 f(x): −10.1 | −10.01 | −10.001 | −9.999 | −9.99 | −9.9 Estimate lim(x→−5) f(x).
Answer
Question 16
g(x) = (x³ + 8)/(x + 2). x: −2.1 | −2.01 | −2.001 | −1.999 | −1.99 | −1.9 g(x): 12.61 | 12.0601 | 12.006 | 11.994 | 11.9401 | 11.41 Estimate lim(x→−2) g(x).
Answer
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