Find the limit by creating a table of values.
Table of contents
- 0. Functions4h 53m
- 1. Limits and Continuity2h 2m
- 2. Intro to Derivatives1h 33m
- 3. Techniques of Differentiation2h 18m
- 4. Derivatives of Exponential & Logarithmic Functions1h 16m
- 5. Applications of Derivatives2h 19m
- 6. Graphical Applications of Derivatives6h 0m
- 7. Antiderivatives & Indefinite Integrals48m
- 8. Definite Integrals4h 36m
- 9. Graphical Applications of Integrals1h 43m
- 10. Integrals of Inverse, Exponential, & Logarithmic Functions21m
- 11. Techniques of Integration2h 7m
- 12. Trigonometric Functions6h 54m
- Angles29m
- Trigonometric Functions on Right Triangles1h 8m
- Solving Right Triangles23m
- Trigonometric Functions on the Unit Circle1h 19m
- Graphs of Sine & Cosine46m
- Graphs of Other Trigonometric Functions32m
- Trigonometric Identities52m
- Derivatives of Trig Functions42m
- Integrals of Basic Trig Functions28m
- Integrals of Other Trig Functions10m
- 13: Intro to Differential Equations2h 23m
- 14. Sequences & Series2h 8m
- 15. Power Series2h 19m
- 16. Probability & Calculus45m
1. Limits and Continuity
Introduction to Limits
Multiple Choice
Find the limit using the graph of f(x)shown.
limx→4f(x)

A
2
B
−2
C
0
D
Unable to determine
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Verified step by step guidance1
Step 1: Understand the problem. We are tasked with finding the limit of f(x) as x approaches 4 using the graph provided. This involves analyzing the behavior of the function f(x) as x gets closer to 4 from both the left and the right sides.
Step 2: Observe the graph near x = 4. Look at the values of f(x) as x approaches 4 from the left (x < 4) and from the right (x > 4). The graph shows a continuous curve leading to a specific y-value near x = 4.
Step 3: Identify the y-value that the graph approaches as x approaches 4. From the graph, trace the curve to see where it converges near x = 4. Note that the open circle at x = 4 indicates the function value at x = 4 is not defined, but the limit depends on the behavior of the graph as x approaches 4.
Step 4: Confirm that the left-hand limit and right-hand limit are equal. Check the graph to ensure that the y-value approached by the function is the same whether x approaches 4 from the left or the right. This confirms the existence of the limit.
Step 5: Conclude the limit. Based on the graph, the y-value that f(x) approaches as x approaches 4 is −2. This is the limit of f(x) as x approaches 4.
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