Calculate these limits$.$ If the limit is or $,$ write infinity or $-$ infinity. If the limit does not exist, write DNE:

Hint: Remember the first thing you check when you are looking at a limit of a quotient is the limit value of the denominator.

If the denominator does not go to $0,$ you should be able to right down the answer immediately.

If the denominator goes to $0,$ but the numerator does not, you will have to check the sign $($

$$

$)$ of the quotient, from both sides if the limit is not one$-$sided.

If both the numerator and the denominator go to $0,$ you have to do the algebraic trick of rationalizing.

So$,$ group your limits into these three forms and work with them one group at a time.

$($a$)$

lim$$t$$pi $/2$

sin t $$

sin $2$ t $+6$cos $2$ t

$2$cos $2$ t

$=$

$2$