Questions: The average cost per tape, in dollars, for a company to produce x sports videotapes is given by the function A(x) = (12x + 50) / x for x > 0. Graph the function on the interval (0, infinity) and complete the following.
A(x) → as x → infinity
A.
B. A(x) → 17 as x → infinity
C. A(x) → 1 as x → infinity
D. A(x) → 0 as x → infinity
Transcript text: The average cost per tape, in dollars, for a company to produce $x$ sports videotapes is given by the function $A(x)=\frac{12 x+50}{x}$ for $x>0$. Graph the function on the interval $(0, \infty)$ and complete the following.
$A(x) \rightarrow$ $\qquad$ as $x \rightarrow \infty$
A.
B.
$A(x) \rightarrow 17$ as $x \rightarrow \infty$
c.
$A(x) \rightarrow 1$ as $x \rightarrow \infty$
D.
$A(x) \rightarrow 0$ as $x \rightarrow \infty$
Solution
Solution Steps
Step 1: Rewrite the function
Given the average cost function A(x) = (12x + 50)/x, we can rewrite this as A(x) = 12 + 50/x.
Step 2: Evaluate the limit as x approaches infinity
We need to find the limit of A(x) as x approaches infinity.
lim(x→∞) A(x) = lim(x→∞) (12 + 50/x)
As x approaches infinity, the term 50/x approaches 0.
Therefore, lim(x→∞) A(x) = 12 + 0 = 12
Step 3: Choose the correct graph and complete the statement
The graph that corresponds to a horizontal asymptote at A(x) = 12 is graph A.