2.3: Basic Limit Laws

Section 2.3 is a short section that just outlines the rules that must be followed for limits. I've never understood how to solve limits until now, so I never knew what the limit laws were or how to use them. The 'laws' basically just show you an easier approach to a problem depending on whether it is an addition/subtraction, or multiplication/division problem.


Problems:


1. Assume that lim f(x) as x approaches 4 = 2 and the lim g(x) as x approaches 4 = 5. Evaluate the limit: lim(3*f(x) = 3*g(x)) as x approaches 4.
     To solve this problem, I broke it up into the limit of 3 * f(x) + the limit of 3 * g(x) both as x approaches 4. Plugging the given numbers in for f(x) and g(x), I had: the limit of 3*2 as x approaches 4 + the limit of 3*5 as x approaches 4. Using the Constant Multiple Law, which basically says that if you have the limit of two numbers multiplied together you can move the first number to the other side of the limit equation so that you have 3*limit as x approaches 4 of f(x). The Constant Multiple Law gave me: 3*limit of 2 as x approaches 4 =6 and 3* the limit of 5 as x approaches 4 = 15.


2. Is it possible to use the Quotient Law to evalue the limit of tan x/ x as x approaches 0?
    Separate this problem using the Quotient Law, it becomes limit of tan x as x approaches 0 divided by the limit of x as x approaches 0. If you were to just plug 0 in for x, the equation would be undefined, meaning that you would have to find another way to solve it. If you were trying to solve this problem, you could use the graphical or numerical method to solve. I used the numerical method and found that the limit was 1, just to make sure that it was at all possible to solve.