Directions: Using the limit process, find the limit of the following function below.
f(x) = 2 – x^2
To find the limit of a function, f(x), as x approaches a certain value, say c, we use the limit process, which involves the following steps:
1. Write down the function: f(x) = 2 - x^2.
2. Determine the limit: We want to find the limit as x approaches a certain value, so let's say x approaches a value c.
3. Replace x with c in the function: f(c) = 2 - c^2.
4. Simplify the expression as much as possible: There isn't much simplification we can do with this function, so we move on to the next step.
5. Use algebraic manipulation or factorization if applicable: In this particular example, we can't factor or manipulate the expression further.
6. Apply the limit process: To find the limit as x approaches c, we need to determine the behavior of the function as x gets closer and closer to c. We can do this by substituting values of x that are very close to c into the function and observing the result.
For example, if c is 1, we can substitute x values close to 1, such as 0.9, 0.99, 0.999, etc., into the function and see what the resulting values are. As x gets closer to 1, the function f(x) = 2 - x^2 gets closer to the value 2 - 1^2 = 1. So, as x approaches 1, the limit of f(x) is 1.
Similarly, you can apply the limit process to find the limit as x approaches other values of c.
Note: The limit process can also involve taking the limit as x approaches positive or negative infinity, in which case you would substitute very large positive or negative values of x into the function and observe the result.