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.
A limit is the value that a function approaches as the input approaches a specific value. It represents the behavior of the function near that specific input.
The properties used to calculate limits are the sum and difference properties, product property, quotient property, power property, and constant multiple property.
The sum and difference properties state that the limit of a sum or difference of two functions is equal to the sum or difference of the limits of the individual functions. In other words, you can calculate the limit of a sum or difference by taking the limit of each function separately and then adding or subtracting the results.
The power property states that the limit of a power of a function is equal to the power of the limit of the function. In other words, to calculate the limit of a function raised to a power, you can take the limit of the function and raise it to the same power.
The constant multiple property states that the limit of a constant times a function is equal to the constant times the limit of the function. In other words, to calculate the limit of a function multiplied by a constant, you can take the limit of the function and then multiply it by the constant.