The discussion revolves around calculating limits using properties of limits, specifically focusing on the limit of the expression (-3x + 1)^2 as x approaches 0.
The discussion includes various interpretations of the limit calculation, with some participants affirming the correctness of the original approach while others suggest alternative presentations. Guidance on formatting for clarity has been offered.
Some participants note that the original poster's method could be presented differently for better clarity, and there is a recurring emphasis on the use of LaTeX for mathematical expressions.
Amen to that!Office_Shredder said:It would be easier to read these if you used latex. It's not that hard to learn and use, if you plan on posting for a while it's worth figuring it out.
In LaTeX, this looks like ##\lim_{x \to 0}(-3x + 1)^2##nycmathguy said:Homework Statement:: Use the properties of limits to find the limits.
Relevant Equations:: N/A
lim (-3x + 1)^2
x→0
Technically, it's better the other way round:nycmathguy said:Homework Statement:: Use the properties of limits to find the limits.
Relevant Equations:: N/A
Use properties of limits to find the limit.
lim (-3x + 1)^2
x→0
[lim (-3x + 1) as x→0 ]^2
[-3•lim(x) as x→0 + lim (1) as x→0]^2
[-3•0 + 1]^2
[0 + 1]^2
[1]^2 = 1
The limit is 1.
Look great.PeroK said:Technically, it's better the other way round:
$$\lim_{x \rightarrow 0} x = 0$$ $$\lim_{x \rightarrow 0} 3x = 3\lim_{x \rightarrow 0} x = 0$$ $$\lim_{x \rightarrow 0} (3x + 1) = \lim_{x \rightarrow 0} 3x +1 = 1$$ $$\lim_{x \rightarrow 0} (3x + 1)^2 = [\lim_{x \rightarrow 0} (3x +1)]^2 = 1^2 = 1$$
Note that the existence and calculation for each limit follows from the previous limit.