Calculating Limits Using Properties

[nycmathguy]

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.

 

[Office_Shredder]

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.

 

[Mark44]

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 $\lim_{x \to 0}(-3x + 1)^2$

 

[PeroK]

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.

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.