Question

For the following function, complete parts (a) through (e) below.

9
1-x
f(x) =
,*# 1,-1
2'
(a) Show that lim f(x) = 0 and lim f(x) = 0. That is, show that y=0
8448
8118
is a horizontal asymptote of f(x).
Given that f(x) =
9
2'
1-x
lim f(x)=
8448
(Simplify your answers.)
and lim 1-x²=, lim f(x)=0.
8448
8448
lim 9
X4+8
2
lim 1-x
8418
As lim 9=
8448

Answer 1

To show that y=0 is a horizontal asymptote of f(x), we need to find the limit of f(x) as x approaches infinity and as x approaches negative infinity. However, the limits are not equal to 0, so y=0 is not a horizontal asymptote of f(x).

Step-by-step explanation:

To show that y=0 is a horizontal asymptote of f(x), we need to find the limit of f(x) as x approaches infinity and as x approaches negative infinity. We can find these limits by simplifying the function:

lim (1-x)/(2) as x approaches infinity = (1-0)/(2) = 1/2

lim (1-x)/(2) as x approaches negative infinity = (1-0)/(2) = 1/2

Since both limits are equal to 1/2, which is not equal to 0, y=0 is not a horizontal asymptote of f(x).