Question

I get a solution of `y=3` but how to solve for this limit?? `lim(x->-4)(3x+12)/(x+4)`

Answer 1

`3`

Explanation:

Substituting in `-4` right away yields

`lim_(x->-4)(3x+12)/(x+4)=(-12+12)/(-4+4)=0/0`

This is an indeterminate form that tells us nothing, so we need to simplify.

`lim_(x->-4)3(cancel(x+4))/(cancel(x+4))=lim_(x->-4)3=3`

The limit is `3.` What value of `x` we're approaching doesn't impact the limit at all in this case, as all terms involving `x` cancel out perfectly in our simplification.