Determine the Value of k for Which Function f is Continuous at x = 2

Let f be the function defined above. For what value of k is f continuous at x=2?

To determine the value of k for which the function f is continuous at x = 2, we need to check if the following conditions are satisfied:

1) The function f is defined at x = 2

To determine the value of k for which the function f is continuous at x = 2, we need to check if the following conditions are satisfied:

1) The function f is defined at x = 2.
2) The left-hand limit of f as x approaches 2 is equal to the value of f at x = 2.
3) The right-hand limit of f as x approaches 2 is equal to the value of f at x = 2.

Let’s start by checking if condition 1 is satisfied. The function f is defined at x = 2 if and only if the equation for f is valid at x = 2. We don’t have the specific equation for f given here, so we cannot determine this condition without further information.

Now, let’s check conditions 2 and 3 using the left-hand and right-hand limits:

1) Left-hand limit: We need to find the limit of f as x approaches 2 from the left-hand side. This can be denoted as:

lim(x→2-) f(x)

2) Right-hand limit: We need to find the limit of f as x approaches 2 from the right-hand side. This can be denoted as:

lim(x→2+) f(x)

To check conditions 2 and 3, we need to know k and the specific form of the function f. Without this information, it is not possible to determine the value of k that would make f continuous at x = 2.

In summary, without more information about the specific equation for f and the value of k, we cannot determine the value of k that would make f continuous at x = 2.

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