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

Answer 1

#3#

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.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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

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