A girl enrolling in typing class type 60(x+1)/x+9 words per minute after x weeks of lesson. Determine the maximum possible number of words the girl can type as time passes

intuitively , as x ---> ∞

(x+1)/(x+9) ---> 1

so lim 60(x+1)/(x+9) , as x --> ∞
= 60

Well, the maximum number of words the girl can type as time passes is infinity. Because no matter how long she practices, there will always be more words she can type. Unless, of course, she becomes so fast that her fingers catch on fire and she becomes the Flash. In that case, she might be able to type infinite words per minute. But I wouldn't recommend it, because flaming fingers can be quite the inconvenience.

To determine the maximum possible number of words the girl can type as time passes, we need to find the limit of the expression as x approaches infinity.

The expression for the number of words typed after x weeks is given by:
60(x+1)/(x+9)

To find the limit as x approaches infinity, divide each term in the expression by the highest power of x:
60(x/x) * (x+1)/x * (1/(x/x)) * (1/(x+9)/x)

Cancel out common factors in each term of the expression:
(60 * 1 * 1) / (1 * 1)

Simplifying the expression:
60/1

Therefore, the maximum possible number of words the girl can type as time passes is 60 words per minute.

To determine the maximum possible number of words the girl can type as time passes, we need to find the maximum value of the expression 60(x + 1) / (x + 9).

To find the maximum value of this expression, we can use calculus. We need to take the derivative of the expression with respect to x, set it equal to 0, and solve for x.

Let's start by finding the derivative:

d/dx (60(x + 1) / (x + 9))

Using the quotient rule, the derivative of the expression is:

[60 * (x + 9) - 60 * (x + 1)] / (x + 9)^2

Simplifying the numerator:

[60x + 540 - 60x - 60] / (x + 9)^2

Combining like terms:

[480] / (x + 9)^2

To find the maximum value, we need to set the derivative equal to 0:

[480] / (x + 9)^2 = 0

Since the numerator is 480, we can see that the derivative is never equal to 0. This means that there is no maximum value for the expression.

Therefore, the girl can type an unlimited number of words as time passes.