Question

PLEASE HELP URGENT!!

Answer 1

This function would be
                1
f(x) = ---------------
             (x-1)^2

What do we know about this fn?  
1) it's even, because of that power "2."
2) All of the graph is above the x-axis.
3) The x-axis is the horiz. asymptote.
4) the vertical line x=1 is the vertical asymptote.
5) as you approach x = 1 from either side (from the left or from the right), the y value will increase without bound.  
6) because of this "without bound" growth, the function has no limit at x = 1.

Answer 2

Answer:

$\lim_{x \to\ 1}\frac{1}{(x-1)^2}=\infty$

vertical asymptote at x=1

Step-by-step explanation:

$\lim_{x \to\ 1}\frac{1}{(x-1)^2}$

First we find out limit approaches from right

$\lim_{x \to\ 1^+}\frac{1}{(x-1)^2}=\infty$

BEcause the denominator is a positive quantity because it has square

we find out limit approaches from right

$\lim_{x \to\ 1^-}\frac{1}{(x-1)^2}=\infty$

so limit is infinity

$\lim_{x \to\ 1}\frac{1}{(x-1)^2}=\infty$

To find out vertical asymotote , we take the denomintor and set it =0

(x-1)^2=0

Take square on both sides

(x-1) = 0

add 1 on both sides

x=1

So vertical asymptote at x=1