Prove: The square of a number that is two more than a multiple of 3 is one more
than a multiple of 3.
(3n + 2)2 = 9n2 + 12n + [?]
In²+ [
+1
In²+
+ [
In+])+1
=
n +
= 1 more than a multiple of 3

Prove (a) cosh2(x) − sinh2(x) = 1 and (b) 1 − tanh 2(x) = sech 2(x). solution (a) cosh2(x) − sinh2(x) = ex + e−x 2 2 − 2 = e2x + 2 + e−2x 4 − = 4 = . (b) we start with the identity proved in part (a): cosh2(x) − sinh2(x) = 1. if we divide both sides by cosh2(x), we get 1 − sinh2(x) cosh2(x) = 1 or 1 − tanh 2(x) = .

15 points what is the end behavior of this graph? & what is the asymptote of this graph?

This venn diagram shows the pizza topping preferences for 9 students