Calculus Unit Test 1A - Limits and Continuity
Flashcard
•
Mathematics
•
10th Grade - University
•
Practice Problem
•
Hard
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1.
FLASHCARD QUESTION
Front
What is a removable discontinuity?
Back
A removable discontinuity occurs at a point where a function is not defined, but can be made continuous by defining or redefining the function at that point.
2.
FLASHCARD QUESTION
Front
What is a non-removable discontinuity?
Back
A non-removable discontinuity is a point where a function is not continuous and cannot be made continuous by redefining the function at that point.
3.
FLASHCARD QUESTION
Front
Define continuity at a point.
Back
A function is continuous at a point x = c if the following three conditions are met: 1) f(c) is defined, 2) the limit of f(x) as x approaches c exists, and 3) the limit equals f(c).
4.
FLASHCARD QUESTION
Front
What does it mean if a limit approaches infinity?
Back
If a limit approaches infinity, it means that as the input values get closer to a certain point, the output values increase without bound.
5.
FLASHCARD QUESTION
Front
Calculate the limit: @@ ext{lim}_{x ightarrow-rac{1}{2}}(3x^2 + 2)@@
Back
The limit is 3(-rac{1}{2})^2 + 2 = 3(rac{1}{4}) + 2 = rac{3}{4} + 2 = rac{11}{4}.
6.
FLASHCARD QUESTION
Front
What is the limit of a constant function?
Back
The limit of a constant function as x approaches any value is simply the constant itself.
7.
FLASHCARD QUESTION
Front
What is the limit of @@ ext{lim}_{x ightarrow-rac{1}{2}}(x^2 - 4)@@?
Back
The limit is (-rac{1}{2})^2 - 4 = rac{1}{4} - 4 = -rac{15}{4}.
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