We are given with a limit and we need to find it's value so let's start !!!!
But , before starting , let's recall an identity which is the <em>main key</em> to answer this question
Consider The limit ;
Now as directly putting the limit will lead to <em>indeterminate form 0/0.</em> So , <em>Rationalizing</em> the <em>numerator</em> i.e multiplying both numerator and denominator by the <em>conjugate of numerator </em>

Using the above algebraic identity ;


Now , here we <em>need</em> to <em>eliminate (√x-2)</em> from the denominator somehow , or the limit will again be <em>indeterminate </em>,so if you think <em>carefully</em> as <em>I thought</em> after <em>seeing the question</em> i.e what if we <em>add 4 and subtract 4</em> in <em>numerator</em> ? So let's try !


Now , using the same above identity ;


Now , take minus sign common in <em>numerator</em> from 2nd term , so that we can <em>take (√x-2) common</em> from both terms

Now , take<em> (√x-2) common</em> in numerator ;

Cancelling the <em>radical</em> that makes our <em>limit again and again</em> <em>indeterminate</em> ;

Now , <em>putting the limit ;</em>

Answer and Step-by-step explanation:
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To find the total of what you sold for each package, you'll need to write two equations. Know that x = paper plate packages and y = utensil packages.
First, x + y = 15 shows that there has to be fifteen packages, and 8x + 5y = 90 shows the $ made from selling a certain number of packages.
Next, you can solve by substitution, so change x + y = 15 to y = 15 - x.
To find our x, substitute the y in 8x + 5y = 90 to get
8x + 5(15 - x) = 90
Distribute: 8x + 75 - 5x = 90
Combine the X's and subtract the 75: 3x = 15
Divide the 3: x = 5
Now with our x, we can put 5 into the original equation x + y = 15 to get 5 + y = 15. Subtracting the 5, we get y = 10.
So, you have delivered 5 paper plate packages and 10 utensil packages.
The factors of 4 are 1, 2, and 4 .
The factors of 9 are 1, 3, and 9 .