Questions: Business: Online Advertising Revenue Suppose that, for a particular social networking company, the annual revenue from rich media advertisements, in millions of dollars, for the years 2007 through 2012 can be approximated with the model R(x)=-x^4+11x^3-39x^2+45x, where x is the number of years from the beginning of 2007. Find each limit. a. lim x→2 P^P(x) b. lim x→0 P(x)

Business: Online Advertising Revenue Suppose that, for a particular social networking company, the annual revenue from rich media advertisements, in millions of dollars, for the years 2007 through 2012 can be approximated with the model R(x)=-x^4+11x^3-39x^2+45x, where x is the number of years from the beginning of 2007. Find each limit.
a. lim x→2 P^P(x)
b. lim x→0 P(x)

Transcript text: Business: Online Advertising Revenue Suppose that, for a particular social networking company, the annual revenue from rich media advertisements, in millions of dollars, for the years 2007 through 2012 can be approximated with the model $R(x)=-x^{4}+11 x^{3}-39 x^{2}+45 x$, where $x$ is the number of years from the beginning of 2007 . Find each limit. a. $\lim _{x \rightarrow 2} P^{P}(x)$ b. $\lim _{x \rightarrow 0} P(x)$

Solution

Solution Steps

Step 1: Identify the Function

The given function is $ R(x) = -x^4 + 11x^3 - 39x^2 + 45x $.

Step 2: Evaluate the Limit as $ x $ Approaches -2

To find $ \lim_{x \to -2} R(x) $, substitute $ x = -2 $ into the function: \[ R(-2) = -(-2)^4 + 11(-2)^3 - 39(-2)^2 + 45(-2) \] \[ = -16 - 88 - 156 - 90 \] \[ = -350 \]

Step 3: Evaluate the Limit as $ x $ Approaches 0

To find $ \lim_{x \to 0} R(x) $, substitute $ x = 0 $ into the function: \[ R(0) = -0^4 + 11(0)^3 - 39(0)^2 + 45(0) \] \[ = 0 \]