Epsilon-delta limit definition 1 | Limits | Differential Calculus | Khan Academy
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Mathematics
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Practice Problem
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Hard
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8 questions
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1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What does the empty circle on the yellow line at point 'a' indicate?
The function stops there.
The function is undefined at that specific point.
The function changes direction.
The function is at its highest value.
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
In the graph shown, what are the horizontal and vertical lines called?
X-axis and Y-axis
Top line and Side line
Left line and Right line
Horizontal line and Vertical line
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What does the yellow line drawn on the graph represent?
The X-axis
The Y-axis
A function (f(x))
A boundary
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
As the values on the X-axis get closer to 'a' from either side, what happens to the corresponding values of f(x) on the Y-axis?
They move away from L.
They stay the same.
They get closer to L.
They become zero.
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
In the context of limits, what does the value 'epsilon' (ε) represent?
The specific input value 'x'.
How close the function's output (f(x)) is to the limit.
The range of input values around 'a'.
The exact value of the limit 'L'.
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
In the example shown, what is the limit of the function f(x) as x approaches 1?
1
0.5
2
It is undefined.
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
If the limit of a function is 2, and you want the function's output to be within 0.5 of this limit, what is the range of possible output values?
From 0.5 to 1.5
From 1.5 to 2.5
From 0.9 to 1.1
Exactly 2
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