Let $$f(x) = \frac{x^2}{x^2 - 1}.$$find the largest integer $n$ so that $f(2) \cdot f(3) \cdot f(4) \cdots f(n-1) \cdot f(n) < 1.98.$

98

Step-by-step explanation:

Let f(x) =

Find the largest integer n so that f(2) * f(3) * f(4) .... * f(n - 1) * f(n) < 1.98

=

=

Observe that the right factor of the numerator cancels out the left factor of the denominator in the next term AND the right factor of the denominator cancels out the left factor of the numerator in the next term. You are left with the following:

2n < 1.98(n + 1)         multiplied (n + 1) on both sides

2n < 1.98n + 1.98      distributed 1.98 into (n + 1)

0.02n < 1.98             subtracted 1.98n from both sides

      n < 99                divided both sides by 0.02

Since all integers must be LESS THAN 99, the greatest integer is 98

i you goofed up when writing this, because hnot is not a word minusf is not either. i cannot answer   because of that.

step-by-step explanation:

whole numbers.

step-by-step explanation:

we are given the average monthly rainfall (in millimeters) model r(m) for the years 1900-2009 as a function of the month number m.

as we can see m is taken for the number of months for years 1900-2009.

we know that number of months can't be a negative number or decimal number or a fraction.

so, the number of months could be only positive whole numbers.

therefore, whole numbers is more appropriate for the domain of r.