Lesson Worksheet: Limits from Tables and Graphs Mathematics • Higher Education

In this worksheet, we will practice evaluating the limit of a function using tables and graphs.

Q1:

Estimate lim๏—โ†’๏Šซ๐‘“(๐‘ฅ) numerically, given that ๐‘“(๐‘ฅ)=๐‘ฅโˆ’25๐‘ฅโˆ’5๏Šจ.

๐‘ฅ4.94.994.999โŸถ5โŸต5.0015.015.1
๐‘“(๐‘ฅ)9.89.989.998โŸถโŸต10.00210.0210.2

Q2:

Determine lim๏โ†’๏Šฆ๏Šฌ๏9๐‘’โˆ’9๐‘ก by evaluating the function at the following values of ๐‘ก: ยฑ0.5, ยฑ0.1, ยฑ0.01, ยฑ0.001, and ยฑ0.0001.

Q3:

Determine lim๏—โ†’๏Šฑ๏Šง๏Šฆ๏Šจ๏Šจโˆ’๐‘ฅ+10๐‘ฅ๐‘ฅโˆ’100, if it exists, by evaluating the function at the following values of ๐‘ฅ: โˆ’9.5, โˆ’9.9, โˆ’9.95, โˆ’9.99, โˆ’9.999, โˆ’9.9999, โˆ’10.5, โˆ’10.1, โˆ’10.05, โˆ’10.01, โˆ’10.001, and โˆ’10.0001, rounding the result to the nearest six decimal places.

  • Aโˆ’10
  • BThe limit does not exist.
  • Cโˆ’12
  • D0

Q4:

Determine the limit as ๐‘ฅโ†’โˆ’1 of the function represented by the graph.

Q5:

Determine the limit as ๐‘ฅโ†’โˆ’3 of the function represented by the graph.

Q6:

If graph shown represents the function ๐‘“(๐‘ฅ)=๐‘ฅโˆ’3, determine lim๏—โ†’๏Šฑ๏Šง๐‘“(๐‘ฅ).

Q7:

Given that the following graph represents the function ๐‘“(๐‘ฅ)=๐‘ฅโˆ’4๐‘ฅ+2๏Šจ, determine lim๏—โ†’๏Šฑ๏Šจ๐‘“(๐‘ฅ).

Q8:

Determine the limit of the function as ๐‘ฅโ†’3.

Q9:

Determine the limit of the function as ๐‘ฅโ†’โˆ’2.

Q10:

Using the graph representing the function ๐‘“(๐‘ฅ)=(๐‘ฅ+3)+2๏Šจ, determine lim๏—โ†’๏Šฑ๏Šฉ๐‘“(๐‘ฅ).

Q11:

Determine the limit as ๐‘ฅโ†’3 of the function represented by the graph.

Q12:

Determine the limit of the function as ๐‘ฅโ†’โˆ’3.

Q13:

If the following graph represents the function ๐‘“(๐‘ฅ)=(๐‘ฅโˆ’1)โˆ’3๏Šฉ, determine lim๏—โ†’๏Šง๐‘“(๐‘ฅ).

Q14:

Using the graph shown, determine lim๏—โ†’๏Šฉ๐‘“(๐‘ฅ).

Q15:

Determine lim๏—โ†’๏Šฎ๐‘“(๐‘ฅ).

  • A8
  • B3
  • C0
  • DThe limit does not exist.

Q16:

Find lim๏—โ†’๏Šช๏Šฉ๏Šจ๐‘ฅโˆ’๐‘ฅ+2๐‘ฅ+7โˆš๐‘ฅ+1 to 4 decimal places by considering ๐‘“(๐‘ฅ)๏Š at ๐‘ฅ=4.1,๐‘ฅ=4.01,๐‘ฅ=4.001,โ€ฆ๏Šง๏Šจ๏Šฉ. What is the first ๐‘› that you can use?

  • A28.1744,๐‘›=6
  • B28.1744,๐‘›=7
  • C28.1744,๐‘›=3
  • D28.1744,๐‘›=5
  • E28.1744,๐‘›=4

Q17:

Determine the limit of the function as ๐‘ฅโ†’1.

Q18:

Determine the limit of the function as ๐‘ฅโ†’1, if it exists.

Q19:

Determine lim๏—โ†’๏Šฆ๐‘“(๐‘ฅ) using the graph below.

Q20:

Find lim๏—โ†’๏Šฑ๏Šฏ๐‘“(๐‘ฅ) if it exists.

  • A5
  • Bโˆ’9
  • CThe limit does not exist.
  • D1

Q21:

Determine the limit as ๐‘ฅโ†’2 of the function represented by the graph.

Q22:

Using the following figure, determine the limit of the function as ๐‘ฅโ†’0.

Q23:

Determine lim๏—โ†’๏Šช๐‘“(๐‘ฅ), if it exists.

Q24:

Find lim๏—โ†’๏Šฆ๐‘“(๐‘ฅ).

Q25:

Determine lim๏—โ†’๏Šฆ๐‘“(๐‘ฅ), if it exists.

  • Aโˆ’1
  • B1
  • Cโˆ’2
  • DThe limit does not exist.

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