lim t>7 F(x) (1/t)−(1/7)/t-7

To find the limit of the given function as t approaches 7, we can simplify the expression first. Let's break it down step by step:

The given expression is:
F(x) * [(1/t) - (1/7)] / (t-7)

Step 1: Simplify the numerator (1/t) - (1/7)
To subtract fractions, we need to find a common denominator. The common denominator for t and 7 is 7t. So, we have:
[(7 - t) / (7t)]

Step 2: Simplify the entire expression
Now, we have:
F(x) * [(7 - t) / (7t)] / (t - 7)

To further simplify, let's cancel out the common factor of (t - 7) in the numerator and denominator:
F(x) * (7 - t) / (7t * (t - 7))

Now, we can take the limit as t approaches 7:
lim t→7 F(x) * (7 - t) / (7t * (t - 7))

At this point, we have simplified the expression as much as we can. To evaluate the limit, we substitute 7 for t in the expression:

F(x) * (7 - 7) / (7 * 7 * (7 - 7))

The expression in the numerator becomes 0, and the denominator is also 0. In this case, we have an indeterminate form (0/0). To tackle this, we need to apply L'Hôpital's rule or find another way to simplify the expression before evaluating the limit.