Question

A company training program determines that, on average, a new employee can do P(x) pieces of work per day after s days of on-the-job training, where P(x) = 90 + 60x x + 5 . Find lim x→5 P(x).

Answer 1

The limit of the function P(x) = 90 + \frac{60x}{x + 5} as x approaches 5 is found by direct substitution, which yields a limit of 120.

Step-by-step explanation:

The student's question is about finding the limit of a function as the variable approaches a certain value. Specifically, the function in question is P(x) = 90 + \frac{60x}{x + 5}, and we want to find limx→5 P(x). To find this limit, we substitute the value of 5 into the function, assuming that the function is continuous at x = 5, and the denominator is not zero at x = 5, which would introduce division by zero. In this case, P(5) yields P(5) = 90 + \frac{60×5}{5 + 5} = 90 + \frac{300}{10} = 90 + 30 = 120. Therefore, the limit as x approaches 5 is 120. This is a common type of question in high school and college

Answer 2

Answer: The value of
`\lim_(x \to 5) P(x)` is 39.

Step-by-step explanation:

Since we have given that

`P(x)=(90+60x)/(x+5)`

where x be the number of days of on the job training.

We need to find the
`\lim_(x \to 5) P(x)`

So, it becomes,

`\lim_(x \to 5) (90+60x)/(x+5)\\\\ =(90+60* 5)/(5+5)\\\\=(90+300)/(10)\\\\=(390)/(10)\\\\=39`

Hence, the value of
`\lim_(x \to 5) P(x)` is 39.