Limits and Continuity Worksheet
Grade 11 Calculus worksheet covering limits, continuity, and related concepts with various question types.
Includes
Standards
Topics
Limits and Continuity Review
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Date:
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Read each question carefully and provide clear, concise answers. Show all your work for full credit.
1. What is the limit of the function f(x) = (x^2 - 4) / (x - 2) as x approaches 2?
0
2
4
Does not exist
2. For a function to be continuous at a point 'c', which of the following conditions must be met?
f(c) is defined
lim f(x) as x->c exists
lim f(x) as x->c = f(c)
All of the above
3. A function is said to be at a point if the limit of the function as x approaches that point exists, and the function's value at that point is equal to the limit.
4. If a function has a hole in its graph, it represents a discontinuity.
5. Consider the function f(x) = |x| / x. Evaluate the left-hand limit, the right-hand limit, and the overall limit as x approaches 0. Is the function continuous at x=0? Explain your reasoning.
6. If a function is differentiable at a point, then it must also be continuous at that point.
True
False
7. A vertical asymptote indicates a point of removable discontinuity.
True
False
8. Determine the value of 'a' that makes the function continuous at x = 3:
f(x) = { ax^2 - 1, if x < 3
{ 2x + 5, if x >= 3