Question

How do you evaluate the limit `(t+4)/(t^2+14t+49)` as t approaches `1`?

Answer 1

By directly substituting `1` for `t`.

Explanation:

The function `f(t)=(t+4)/(t^2+14t+49)` is defined at `t=1`.

In fact, we can see that `f(t)=(t+4)/(t+7)^2`, so the only time this is undefined is at `t=-7`. To find the limit, just plug `1` into the expression.

`lim_(trarr1)(t+4)/(t^2+14t+49)=(1+4)/(1^2+14(1)+49)=5/64`