2 min readβ’june 7, 2020

Anusha Tekumulla

π₯**Watch: AP Calculus AB/BC - ****Graphical Limits**

This topic centers around the difference between the **value a function is approaching (limits)** and the **value of the function itself**. **Graphs **are a great way to help visualize the difference between these two concepts.

In the graph above, we can show the difference between the value a function is approaching and the actual value of the function. Starting on the left side of the function and moving toward x = 4, we can see that the y value gets closer to y = 5. Starting on the right side and moving backward to x = 4, we also get closer to y = 5. However, if we try to evaluate the function AT x = 4 we get y = 4. This is the key difference between the value a function is approaching and the value of the function itself. In this example, **the limit is 5** but **the value of f(4) is 4**.Β π€

The big takeaway from this example is that the value of a function at a particular value does not (β) mean that the limit value is the same.

As you saw in the example above, we estimate a limit value in a graph by approaching the x value from both sides. Here are the steps needed to estimate the limit value:Β

- First, we approach the x value from the left side.Β
- After getting a y value from the left side, approach the x value from the right side.Β
- If the y values from the left side and the right side are the same, we say that the limit is that y value. If the values arenβt equal, we say that the limit does not exist.Β

If youβre still confused, take a look at the pictures below.Β π·

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πUnit 1 β Limits & Continuity

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π₯Unit 6 β Integration & Accumulation of Change

πUnit 7 β Differential Equations

πΆUnit 8 β Applications of Integration

π¦Unit 9 β Parametric Equations, Polar Coordinates, & Vector-Valued Functions (BC Only)

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