Use graphs and tables to find the limit and identify any vertical asymptotes of the function. limit of 1 divided by the quantity x minus 1 squared as x approaches 1

Limit: infinite

vertical asymptote: x=1

Step-by-step explanation:

To find the limit, you can graph 1 divided by x minus 1 squared on desmos and set x=1, and you should see that the function never touches x=1 making it infinite.

To find the vertical asymptote set the denominator equal to 0 then solve, so (x-1) ^2=0, take the square root of both sides, x-1=0, add 1, x=1.

We are given the function: 1 divided by the quantity x minus 2 squared and is asked in the problem to determine the limit of x as x approaches 2 as well as vertical asymptotes if there are any. To find the limit, we just have to substitute the equation with the value of the numerical limit. The equation then becomes, 1 / (x-2) ^2 = 1 / (2-2) ^2 = 1/0. Any number divided by zero is equal to infinity so the limit is infinity. A vertical asymptote is the value of x in which the denominator becomes zero, that is (x-2) ^2 = 0; x = 2. The vertical asymptote is equal to 2.