Functions, Graphs, and Limits - AP Calculus BC

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

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

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 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 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 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

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 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 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 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 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 piecewise function

indicates that is one when is less than five, and is zero if the variable is greater than five. At , there is a hole at the end of the split.

The limit does not indicate whether we want to find the limit from the left or right, which means that it is necessary to check the limit from the left and right. From the left to right, the limit approaches 1 as approaches negative five. From the right, the limit approaches zero as approaches negative five.

Since the limits do not coincide, the limit does not exist for .

The piecewise function

indicates that is one when is less than five, and is zero if the variable is greater than five. At , there is a hole at the end of the split.

The limit does not indicate whether we want to find the limit from the left or right, which means that it is necessary to check the limit from the left and right. From the left to right, the limit approaches 1 as approaches negative five. From the right, the limit approaches zero as approaches negative five.

Since the limits do not coincide, the limit does not exist for .

The piecewise function

indicates that is one when is less than five, and is zero if the variable is greater than five. At , there is a hole at the end of the split.

The limit does not indicate whether we want to find the limit from the left or right, which means that it is necessary to check the limit from the left and right. From the left to right, the limit approaches 1 as approaches negative five. From the right, the limit approaches zero as approaches negative five.

Since the limits do not coincide, the limit does not exist for .

The piecewise function

indicates that is one when is less than five, and is zero if the variable is greater than five. At , there is a hole at the end of the split.

The limit does not indicate whether we want to find the limit from the left or right, which means that it is necessary to check the limit from the left and right. From the left to right, the limit approaches 1 as approaches negative five. From the right, the limit approaches zero as approaches negative five.

Since the limits do not coincide, the limit does not exist for .

The piecewise function

indicates that is one when is less than five, and is zero if the variable is greater than five. At , there is a hole at the end of the split.

The limit does not indicate whether we want to find the limit from the left or right, which means that it is necessary to check the limit from the left and right. From the left to right, the limit approaches 1 as approaches negative five. From the right, the limit approaches zero as approaches negative five.

Since the limits do not coincide, the limit does not exist for .

The piecewise function

indicates that is one when is less than five, and is zero if the variable is greater than five. At , there is a hole at the end of the split.

The limit does not indicate whether we want to find the limit from the left or right, which means that it is necessary to check the limit from the left and right. From the left to right, the limit approaches 1 as approaches negative five. From the right, the limit approaches zero as approaches negative five.

Since the limits do not coincide, the limit does not exist for .