Estimate a limit from a table of values

Question 1

f(x) = (x² − 36)/(x − 6). It has no value at x = 6 itself. x: 5.9 | 5.99 | 5.999 | 6.001 | 6.01 | 6.1 f(x): 11.9 | 11.99 | 11.999 | 12.001 | 12.01 | 12.1 Estimate lim(x→6) f(x).

Answer 

Question 2

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).

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Question 3

x: −0.1 | −0.01 | −0.001 | 0.001 | 0.01 | 0.1 f(x): −1 | −1 | −1 | 1 | 1 | 1 Does lim(x→0) f(x) exist?

• A. Yes
• B. No: the two sides approach different values

Question 4

f(x) = (x² − 36)/(x − 6). It has no value at x = 6 itself. x: 5.9 | 5.99 | 5.999 | 6.001 | 6.01 | 6.1 f(x): 11.9 | 11.99 | 11.999 | 12.001 | 12.01 | 12.1 Estimate lim(x→6) f(x).

Answer 

Question 5

g(x) = (x³ − 27)/(x − 3). x: 2.9 | 2.99 | 2.999 | 3.001 | 3.01 | 3.1 g(x): 26.11 | 26.9101 | 26.991 | 27.009 | 27.0901 | 27.91 Estimate lim(x→3) g(x).

Answer 

Question 6

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 Does lim(x→−1) f(x) exist?

• A. Yes
• B. No: the two sides approach different values

Question 7

f(x) = (x² − 16)/(x − 4). It has no value at x = 4 itself. x: 3.9 | 3.99 | 3.999 | 4.001 | 4.01 | 4.1 f(x): 7.9 | 7.99 | 7.999 | 8.001 | 8.01 | 8.1 Estimate lim(x→4) f(x).

Answer 

Question 8

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).

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Question 9

x: 1.9 | 1.99 | 1.999 | 2.001 | 2.01 | 2.1 f(x): 3.9 | 3.99 | 3.999 | 4.001 | 4.01 | 4.1 Does lim(x→2) f(x) exist?

• A. Yes
• B. No: the two sides approach different values

Question 10

f(x) = (x² − 25)/(x − 5). It has no value at x = 5 itself. x: 4.9 | 4.99 | 4.999 | 5.001 | 5.01 | 5.1 f(x): 9.9 | 9.99 | 9.999 | 10.001 | 10.01 | 10.1 Estimate lim(x→5) f(x).

Answer 

Question 11

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 12

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 Does lim(x→3) f(x) exist?

• A. Yes
• B. No: the two sides approach different values

Question 13

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 14

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).

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Question 15

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 16

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