# Properties of Limits

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

^2 = 1

The limit is 1.

Staff Emeritus
Gold Member
Looks good to me.

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.

• SammyS
Mentor
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.
Amen to that!

Homework Statement:: Use the properties of limits to find the limits.
Relevant Equations:: N/A

lim (-3x + 1)^2
x→0
In LaTeX, this looks like ##\lim_{x \to 0}(-3x + 1)^2##
In rendered form it is ##\lim_{x \to 0}(-3x + 1)^2##

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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

^2 = 1

The limit is 1.
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.

• nycmathguy
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.
Look great.