Tutor profile: Haofei B.

lim x-->2 (x^2 - 4) / (x-2) = ?

What answer do you come up with? It doesn't exist because x cannot equal 2? Let's simplify this question (x^2 - 4)=(x + 2) ( x - 2 ). Hence, (x^2-4) / (x - 2) = x + 2. As a result, as x goes extremely close to 2, the limit equals 2+2 = 4;

Four people each own a hat. If the hats are assigned to the four people at random, what is the probability that everyone gets back their own hat?

The probability= divide the number of events by the number of possible outcomes The number of events is one because there is only one way that they can get back their own hats. How many ways can we arrange those hats? By permutation: the number of ways putting 4 hats in order is 4! P(gets back their own hat)=1/(4!)=0.042

Could you find the root for x^2+4x+4=0?

1. (a+b)^2=a^2+b^2+2ab We can approach this question using this formula which a = x, b = 2 in this case. (x+2)^2=0 than we have absolute value |x+2|=0 Hence, the result it x=2 or x=-2;