The limit of the function (-3x + 1)^2 as x approaches 0 is calculated using properties of limits, resulting in a final value of 1. The calculation involves breaking down the limit into its components: lim(-3x + 1) as x approaches 0, which simplifies to 1, and then squaring that result. The discussion emphasizes the importance of using LaTeX for clarity in mathematical expressions, particularly when posting complex calculations in forums.
PREREQUISITESStudents studying calculus, educators teaching limit concepts, and anyone interested in improving their mathematical communication skills through LaTeX.
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.