How to find the value k that makes the function continuous

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Mathematics
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11th Grade - University
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Hard
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5 questions
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1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is required for a function to be continuous at a point?
The function must be differentiable at that point.
The function must have a maximum at that point.
The left-hand limit and right-hand limit must be equal.
The function must be defined for all real numbers.
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What happens if the left-hand and right-hand limits of a function are not equal?
The function is continuous.
The function has a local maximum.
The function is differentiable.
The function is not continuous.
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
How can you evaluate the limit of a continuous function as x approaches a point?
By directly substituting the point into the function.
By using L'Hôpital's rule.
By calculating the area under the curve.
By finding the derivative at that point.
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
In the example discussed, what is the value of K that makes the piecewise function continuous?
K = 1
K = 0
K = 2
K = -1
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What type of graph would you expect if a piecewise function is continuous at a point?
A graph with a jump discontinuity.
A graph with a hole at that point.
A graph with a vertical asymptote.
A smooth, connected graph.
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