Use graphs and tables to find the limit and identify any vertical asymptotes of limit of 1 divided by the quantity x minus 7 squared as x approaches 7.

The given function is :

For finding the required limit : We use the following property of limits

Now, if approaching from left (x-7) < 0 but its square is positive So the whole limit becomes +∞

If approaching from right (x - 7)_> 0 and its square also positive so the whole limit equals +∞

Hence, the required limit is +∞

Now, to find the vertical asymptote : check the value at which the function is not defined.

At x = 7 the denominator becomes 0 and the function is not defined so x = 7 is the vertical asymptote of the given function.

step-by-step explanation:

step-by-step :