{"id":260990,"date":"2024-05-03T04:19:49","date_gmt":"2024-05-03T04:19:49","guid":{"rendered":"https:\/\/namso-gen.co\/blog\/?p=260990"},"modified":"2024-05-03T04:19:49","modified_gmt":"2024-05-03T04:19:49","slug":"how-to-find-y-value-of-removable-discontinuity","status":"publish","type":"post","link":"https:\/\/namso-gen.co\/blog\/how-to-find-y-value-of-removable-discontinuity\/","title":{"rendered":"How to find Y value of removable discontinuity?"},"content":{"rendered":"

**How to find Y value of removable discontinuity?**<\/p>\n

When dealing with functions, it is important to identify any points of discontinuity to understand the behavior of the function. A removable discontinuity occurs when there is a hole in the graph of a function at a particular x-value. The y-value of this hole, also known as the limit of the function at that point, can be determined by following a few simple steps. Let’s explore how to find the y-value of a removable discontinuity.<\/p>\n

To find the y-value of a removable discontinuity, we need to consider the left and right limits of the function at the given x-value. The y-value will be the same as those limits since, at the point of discontinuity, the function can be made continuous by assigning the value of the limits to that point.<\/p>\n

1. **Step 1: Identify the point of discontinuity**
\n Determine the x-value at which the discontinuity exists. This can usually be done by analyzing the function or graph given.<\/p>\n

2. **Step 2: Calculate the left limit**
\n Find the limit of the function as x approaches the point of discontinuity from the left side. This can be done by substituting values slightly less than the x-value into the function and observe the trend of the outputs.<\/p>\n

3. **Step 3: Calculate the right limit**
\n Similarly, calculate the limit of the function as x approaches the point of discontinuity from the right side. Substitute values slightly greater than the x-value into the function and analyze the outputs.<\/p>\n

4. **Step 4: Determine the y-value**
\n If the left and right limits from steps 2 and 3 are equal, then the y-value of the removable discontinuity is the same as these limits. Assign that value to the corresponding x.<\/p>\n

Let’s consider an example to illustrate the process:<\/p>\n

Example: Find the y-value of the removable discontinuity for the function f(x) = (x^2 – 9) \/ (x – 3).<\/p>\n

Step 1: The point of discontinuity is x = 3.<\/p>\n

Step 2: Left limit calculation
\n Let’s approach 3 from the left side, using x = 2.9, 2.99, 2.999 as inputs.
\n As these x-values approach 3, the output values of the function approach 6.
\n Therefore, the left limit is 6.<\/p>\n

Step 3: Right limit calculation
\n Let’s approach 3 from the right side, using x = 3.1, 3.01, 3.001 as inputs.
\n As these x-values approach 3, the output values approach 6.
\n Hence, the right limit is 6.<\/p>\n

Step 4: Since the left and right limits are both 6, the y-value of the removable discontinuity at x = 3 is 6.<\/p>\n

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