Find the indicated limit$.$

lim$$

t$9$

$(9$t$22$t $+1)$

Step $1$

We are to find the limit of a quadratic expression. We can use this theorem on the Properties of Limits to evaluate the limit algebraically by rewriting as a combination of simpler limits$.$

Property $3$ states that the limit of a sum or difference is equal to the sum or difference of the limits$.$

lim$$

x$$a$$

$[$f$($x$)$ g$($x$)]=$

lim$$

x$$a$$

f$($x$)$

lim$$

x$$a$$

g$($x$)$

Using this property repeatedly, we can write the given limit as three simpler limits$.$

lim$$

t$9$

$(9$t$22$t $+1)=$

lim$$

t$9$

$9$t$2$

lim$$

t$9$

$+$

lim$$

t$9$

$1$