How do you find the limit of $(x+3)^2007$ as $x->-4$ ?

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Answer 1 · 2016-11-25T18:13:48

$lim_(x rarr -4) (x+3)^2007= -1$

Let $f(x)=(x+3)^2007$ ,

Then $f(x)$ is a continuous function so,

$lim_(x rarr c)=f(c) AA c in RR$

$:. lim_(x rarr -4) f(x) = f(-1) = (-1)^2007$

Now $(-1)^(2n) = +1$ , and $(-1)^(2n+1) = -1 AA n in NN$

Hence $(-1)^2007 = -1$ , and so:

$lim_(x rarr -4) (x+3)^2007= -1$

How do you find the limit of (x+3)^2007(x+3)^2007 as x->-4x->-4?