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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

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

Answer :

Final answer:

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).

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).

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