Calculate each of the following limits:
1.) lim(x^2+6x-5)
x-2

2.) lim(x^2-16)/(x+4)
x--4

Question

Calculate each of the following limits:
1.) lim(x^2+6x-5)
     x->2

2.) lim(x^2-16)/(x+4)
     x->-4

anonymous · Answer

factor, cancel, replace $x$ by $-4$ for the second one

anonymous · Answer

first one plug in the number, see what you get

anonymous · Answer

i.e. compute 
$$2^2+6\times 2-5$$

anonymous · Answer

So then the first one would 11

anonymous · Answer

The first one can be done with plain substituion, i.e. just plug in 2 and evaluate.

The second one requires some factoring and cancellation like this:$$\bf \lim_{x \rightarrow -4}\frac{ x^2-16 }{ x+4 }= \lim_{x \rightarrow -4}\frac{ (x-4)\cancel{(x+4)} }{\cancel{ x+4} }\lim_{x \rightarrow -4}= x-4$$

anonymous · Answer

yes

anonymous · Answer

The equal sign before x-4 isn't supposed to be there lol.

anonymous · Answer

And substitute once again.

anonymous · Answer

okay. I see it, so its...simple, once again.