Question

1.For each of the following find:

I. limit of f(x) as x approaches a^-

II. limit of f(x) as x approaches a^+

II. limit of f(x) as x approaches a

1A.
f(x) = (absolute value of (x^2+3x+2))/(x^2-4); a=2

1B.f(x)= sin x if x < pi/6
f(x) =tan x if x=pi/6 a=pi/6
f(x)= cos x if x>.pi/6

1C. f(x)=sin x/3 if x
9 years ago

Answer 1

\[\lim_{x \rightarrow 2^-}\frac{|x^2+3x+2|}{x^2-4}\]

Answer 2

is that the correct first question?

Answer 3

Yes

Answer 4

Well if it is you can write the absolute value part as a piecewise function to help you find what is going on around 2 from the left...
I think it is easy to factor (x^2+3x+2)
to find the absolute value of that flip the negative about about the x-axis
so actually the part between -2 and -1 is the opposite of (x^2+3x+2)
or -(x^2+3x+2)
that is
|x^2+3x+2|=x^2+3x+2 if x>-1 or x<-2
|x^2+3x+2|=-(x^2+3x+2) if -2<x<-1