Question

Find the limit…………………….

Answer 1

`(1)/(22)`

Explanation:

Limits:

For these time of limit problems, we want to try to rewrite the equation in such a way that we can get some value, because in this case plugging in x=121, we simply get 0/0 which is indeterminate.

One thing you may or may not notice is that 11 and 121 are closely related, as 121 is just the square of 11... something important to solving this.

We have the fraction:
`√(x)-11`, we want to possibly rewrite this into the denominator (x-121) to cancel out the two... well we can use the difference of squares.
`(√(x)-11)(√(x)+11)=x-121` and we want to multiply the bottom by this amount as well, giving us the fraction:

`(x-121)/((x-121)(√(x)+11)`

Now we can cancel out the x-121 from the numerator and denominator, leaving us with:

`(1)/(√(x)+11)`

and now we can directly plug in 121

`(1)/(√(121)+11)=(1)/(11+11)=(1)/(22)`