Functions, Graphs, and Limits - AP Calculus BC
Card 1 of 1344
Evaluate the following limit:
Evaluate the following limit:
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The limit we are given is one sided, meaning we are approaching our x value from one side; in this case, the negative sign exponent indicates that we are approaching 3 from the left side, or using values slightly less than three on approach.
This corresponds to the part of the piecewise function for values less than 3. When we substitute our x value being approached, we get
The limit we are given is one sided, meaning we are approaching our x value from one side; in this case, the negative sign exponent indicates that we are approaching 3 from the left side, or using values slightly less than three on approach.
This corresponds to the part of the piecewise function for values less than 3. When we substitute our x value being approached, we get
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Evaluate the following limit:
Evaluate the following limit:
Tap to reveal answer
The limit we are given is one sided, meaning we are approaching our x value from one side; in this case, the negative sign exponent indicates that we are approaching 3 from the left side, or using values slightly less than three on approach.
This corresponds to the part of the piecewise function for values less than 3. When we substitute our x value being approached, we get
The limit we are given is one sided, meaning we are approaching our x value from one side; in this case, the negative sign exponent indicates that we are approaching 3 from the left side, or using values slightly less than three on approach.
This corresponds to the part of the piecewise function for values less than 3. When we substitute our x value being approached, we get
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For the piecewise function:
, find 
.
For the piecewise function:
Tap to reveal answer
The limit 
indicates that we are trying to find the value of the limit as 
approaches to zero from the right side of the graph.
From right to left approaching 
, the limit approaches to 1 even though the value at 
of the piecewise function does not exist.
The answer is 
.
The limit
From right to left approaching
The answer is
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Evaluate the following limit:
Evaluate the following limit:
Tap to reveal answer
The limit we are given is one sided, meaning we are approaching our x value from one side; in this case, the negative sign exponent indicates that we are approaching 3 from the left side, or using values slightly less than three on approach.
This corresponds to the part of the piecewise function for values less than 3. When we substitute our x value being approached, we get
The limit we are given is one sided, meaning we are approaching our x value from one side; in this case, the negative sign exponent indicates that we are approaching 3 from the left side, or using values slightly less than three on approach.
This corresponds to the part of the piecewise function for values less than 3. When we substitute our x value being approached, we get
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For the piecewise function:
, find .
For the piecewise function:
Tap to reveal answer
The limit indicates that we are trying to find the value of the limit as approaches to zero from the right side of the graph.
From right to left approaching , the limit approaches to 1 even though the value at of the piecewise function does not exist.
The answer is .
The limit
From right to left approaching
The answer is
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Evaluate the following limit:
Evaluate the following limit:
Tap to reveal answer
The limit we are given is one sided, meaning we are approaching our x value from one side; in this case, the negative sign exponent indicates that we are approaching 3 from the left side, or using values slightly less than three on approach.
This corresponds to the part of the piecewise function for values less than 3. When we substitute our x value being approached, we get
The limit we are given is one sided, meaning we are approaching our x value from one side; in this case, the negative sign exponent indicates that we are approaching 3 from the left side, or using values slightly less than three on approach.
This corresponds to the part of the piecewise function for values less than 3. When we substitute our x value being approached, we get
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Evaluate the following limit:
Evaluate the following limit:
Tap to reveal answer
The limit we are given is one sided, meaning we are approaching our x value from one side; in this case, the negative sign exponent indicates that we are approaching 3 from the left side, or using values slightly less than three on approach.
This corresponds to the part of the piecewise function for values less than 3. When we substitute our x value being approached, we get
The limit we are given is one sided, meaning we are approaching our x value from one side; in this case, the negative sign exponent indicates that we are approaching 3 from the left side, or using values slightly less than three on approach.
This corresponds to the part of the piecewise function for values less than 3. When we substitute our x value being approached, we get
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For the piecewise function:
, find .
For the piecewise function:
Tap to reveal answer
The limit indicates that we are trying to find the value of the limit as approaches to zero from the right side of the graph.
From right to left approaching , the limit approaches to 1 even though the value at of the piecewise function does not exist.
The answer is .
The limit
From right to left approaching
The answer is
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For the piecewise function:
, find .
For the piecewise function:
Tap to reveal answer
The limit indicates that we are trying to find the value of the limit as approaches to zero from the right side of the graph.
From right to left approaching , the limit approaches to 1 even though the value at of the piecewise function does not exist.
The answer is .
The limit
From right to left approaching
The answer is
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Evaluate the following limit:
Evaluate the following limit:
Tap to reveal answer
The limit we are given is one sided, meaning we are approaching our x value from one side; in this case, the negative sign exponent indicates that we are approaching 3 from the left side, or using values slightly less than three on approach.
This corresponds to the part of the piecewise function for values less than 3. When we substitute our x value being approached, we get
The limit we are given is one sided, meaning we are approaching our x value from one side; in this case, the negative sign exponent indicates that we are approaching 3 from the left side, or using values slightly less than three on approach.
This corresponds to the part of the piecewise function for values less than 3. When we substitute our x value being approached, we get
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For the piecewise function:
, find .
For the piecewise function:
Tap to reveal answer
The limit indicates that we are trying to find the value of the limit as approaches to zero from the right side of the graph.
From right to left approaching , the limit approaches to 1 even though the value at of the piecewise function does not exist.
The answer is .
The limit
From right to left approaching
The answer is
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Evaluate the following limit:
Evaluate the following limit:
Tap to reveal answer
The limit we are given is one sided, meaning we are approaching our x value from one side; in this case, the negative sign exponent indicates that we are approaching 3 from the left side, or using values slightly less than three on approach.
This corresponds to the part of the piecewise function for values less than 3. When we substitute our x value being approached, we get
The limit we are given is one sided, meaning we are approaching our x value from one side; in this case, the negative sign exponent indicates that we are approaching 3 from the left side, or using values slightly less than three on approach.
This corresponds to the part of the piecewise function for values less than 3. When we substitute our x value being approached, we get
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For the piecewise function:
, find .
For the piecewise function:
Tap to reveal answer
The limit indicates that we are trying to find the value of the limit as approaches to zero from the right side of the graph.
From right to left approaching , the limit approaches to 1 even though the value at of the piecewise function does not exist.
The answer is .
The limit
From right to left approaching
The answer is
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For the piecewise function:
, find .
For the piecewise function:
Tap to reveal answer
The limit indicates that we are trying to find the value of the limit as approaches to zero from the right side of the graph.
From right to left approaching , the limit approaches to 1 even though the value at of the piecewise function does not exist.
The answer is .
The limit
From right to left approaching
The answer is
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For the piecewise function:
, find .
For the piecewise function:
Tap to reveal answer
The limit indicates that we are trying to find the value of the limit as approaches to zero from the right side of the graph.
From right to left approaching , the limit approaches to 1 even though the value at of the piecewise function does not exist.
The answer is .
The limit
From right to left approaching
The answer is
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Evaluate the following limit:
Evaluate the following limit:
Tap to reveal answer
The limit we are given is one sided, meaning we are approaching our x value from one side; in this case, the negative sign exponent indicates that we are approaching 3 from the left side, or using values slightly less than three on approach.
This corresponds to the part of the piecewise function for values less than 3. When we substitute our x value being approached, we get
The limit we are given is one sided, meaning we are approaching our x value from one side; in this case, the negative sign exponent indicates that we are approaching 3 from the left side, or using values slightly less than three on approach.
This corresponds to the part of the piecewise function for values less than 3. When we substitute our x value being approached, we get
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For the piecewise function:
, find .
For the piecewise function:
Tap to reveal answer
The limit indicates that we are trying to find the value of the limit as approaches to zero from the right side of the graph.
From right to left approaching , the limit approaches to 1 even though the value at of the piecewise function does not exist.
The answer is .
The limit
From right to left approaching
The answer is
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Evaluate the following limit:
Evaluate the following limit:
Tap to reveal answer
The limit we are given is one sided, meaning we are approaching our x value from one side; in this case, the negative sign exponent indicates that we are approaching 3 from the left side, or using values slightly less than three on approach.
This corresponds to the part of the piecewise function for values less than 3. When we substitute our x value being approached, we get
The limit we are given is one sided, meaning we are approaching our x value from one side; in this case, the negative sign exponent indicates that we are approaching 3 from the left side, or using values slightly less than three on approach.
This corresponds to the part of the piecewise function for values less than 3. When we substitute our x value being approached, we get
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Evaluate the following limit:
Evaluate the following limit:
Tap to reveal answer
The limit we are given is one sided, meaning we are approaching our x value from one side; in this case, the negative sign exponent indicates that we are approaching 3 from the left side, or using values slightly less than three on approach.
This corresponds to the part of the piecewise function for values less than 3. When we substitute our x value being approached, we get
The limit we are given is one sided, meaning we are approaching our x value from one side; in this case, the negative sign exponent indicates that we are approaching 3 from the left side, or using values slightly less than three on approach.
This corresponds to the part of the piecewise function for values less than 3. When we substitute our x value being approached, we get
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For the piecewise function:
, find .
For the piecewise function:
Tap to reveal answer
The limit indicates that we are trying to find the value of the limit as approaches to zero from the right side of the graph.
From right to left approaching , the limit approaches to 1 even though the value at of the piecewise function does not exist.
The answer is .
The limit
From right to left approaching
The answer is
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