Limits from graphs and tables
Grade 12 Math Worksheet - Building Confidence
Circle the best answer, or write your answer on the line.
Read this first
Table, time t in seconds and speed in m/s
t = 1.9 gives 4.5; t = 1.99 gives 4.95; t = 1.999 gives 4.995; t = 2.001 gives 5.005; t = 2.01 gives 5.05; t = 2.1 gives 5.5. At t = 2 exactly the reading is 3.
A cart's speed sensor gives the table shown near t = 2. Ari reads it from both sides. What is the limit of the reading as t approaches 2?
Table, time t in minutes and depth in cm
t = 3.9 gives 9; t = 3.99 gives 11.7; t = 3.999 gives 11.97; t = 4.001 gives 12.03; t = 4.01 gives 12.3; t = 4.1 gives 15. At t = 4 exactly the reading is 0.
A tank's depth gauge gives the table shown near t = 4. Bo reads it from both sides. What is the limit of the reading as t approaches 4?
Table, time t in minutes and temperature in °C
t = 9.9 gives 63.5; t = 9.99 gives 62.15; t = 9.999 gives 62.015; t = 10.001 gives 61.985; t = 10.01 gives 61.85; t = 10.1 gives 60.5. At t = 10 exactly the reading is 75.
A coffee thermometer gives the table shown near t = 10. Esme reads it from both sides. What is the limit of the reading as t approaches 10?
Kira traces the graph shown toward x = 2 from the left. What is the limit of f(x) as x → 2⁻?
Luz traces the graph shown toward x = 1 from the right. What is the limit of f(x) as x → 1⁺?
Milo traces the graph shown toward x = 3 from the left. What is the limit of f(x) as x → 3⁻?
Noah traces the graph shown toward x = -1 from the right. What is the limit of f(x) as x → -1⁺?
Table, distance in m and height in m
x = 4.9 gives 2.8; x = 4.99 gives 2.98; x = 4.999 gives 2.998; x = 5.001 gives 6.997; x = 5.01 gives 6.97; x = 5.1 gives 6.7. At x = 5 exactly the reading is 4.
A ramp sensor gives the table shown, which jumps at x = 5. Pia reads it from the right. What is the limit as x → 5⁺?
Table, time in hours and depth in dm
x = 1.9 gives 9.8; x = 1.99 gives 9.98; x = 1.999 gives 9.998; x = 2.001 gives 5.997; x = 2.01 gives 5.97; x = 2.1 gives 5.7. At x = 2 exactly the reading is 8.
A pool's water gauge gives the table shown, which jumps at x = 2. Ren reads it from the left. What is the limit as x → 2⁻?
Table, time in hours and temperature in °C
x = 5.9 gives -1.2; x = 5.99 gives -1.02; x = 5.999 gives -1.002; x = 6.001 gives 1.997; x = 6.01 gives 1.97; x = 6.1 gives 1.7. At x = 6 exactly the reading is 0.
A thermometer outside gives the table shown, which jumps at x = 6. Tala reads it from the right. What is the limit as x → 6⁺?