what is the procedure to evaluate limits without a calculator?

Question

please explain in detail the steps to solve this problem.

lim (x^2-4) / (x^2 +4) as x approaches 2

p.s. i knew how to do this, its for a review but i just can't remember.

Answer 1

This is a simple limit to evaluate, and should have been the first type you learned.

Whenever your variable in the limit approaches a value at which the expression is defined, simply plug in the limit value to get your limit. Thus, for this question, since x->2, you simply have to plug 2 in for x to get your answer of 0.

Answer 2

simplify

x^2-4 becomes (x+2)(x-2)/x^2+4

if you have a graphing calculator just graph it....since the top is 0 when 2 is plugged in i'd guess that's the answer

something is telling me that you switched the numerator and denominator

Answer 3

you get zero.

to put it simply...(we'll use non-technical terms)
1. plug in '2' into your 'x's (which gives you...)

2^2-4 / 2^2+4

2. you'll get 0/4, which gives you 0...

Answer 4

put the value of x
u get 0/8=0
so answer is 0