Basic forms from Calculus. -----> LIMITS

1: 1.- Definition of a Limit.

Limit of f(x) when x--->a = L <===> for all ε > 0 there exist a δ such that if 0< lx-al < δ then l f(x) - L l < ε

Limit of f(x) when x--->a = L <===> for each ε < 0 there exist a δ such that if if 0< lx-al < δ then l f(x) - L l < ε

Limit of f(x) when x--->a = L <===> for each ε > 0 there exist a δ such that if if 0 > lx-al > δ then l f(x) - L l < ε

Limit of f(x) when x--->a = L <===> for all ε < 0 there exist a δ such that if if 0 > lx-al > δ then l f(x) - L l < ε

2: 2.- Limit of a Constant? (K)

Limit of K when x-->a = a

Limit of K when x-->a = x

Limit of K when x-->a = f(x)

Limit of K when x-->a = K

3: 3.- Linear Functions? (quite literally just a line)

Limit of x when x-->a = a

Limit of x when x-->a = f(x)

Limit of x when x-->a = x

Limit of x when x-->a = K

4: 4.- Limit of Exponentials.

Limit of x^{n} when x-->a = a^{n}

Limit of x^{n} when x-->a = x^{n}

Limit of x^{n} when x-->a = K^{n}

5: 5.- Limit with "Constant Multiplier."

Limit of [Kf(x)] when x-->a = Limit of K

Limit of [Kf(x)] when x-->a = Limit[k] * Limit[f(x)]

Limit of [Kf(x)] when x-->a = K[Limit of f(x)]

Limit of [Kf(x)] when x-->a = Limit[f(x)]

6: 6.- Limit of a Sum or Difference Rule.

Limit of [ f(x) ± g(x) ] when x -->a = Limit of [ f(x) + g(x) ] or Limit of [ f(x) - g(x) ]

Limit of [ f(x) ± g(x) ] when x -->a = Lim[f(x)] ± Lim[g(x)}

7: 7.- Since addition is "axiomatic" could you derivate Forms 7# and 9#?

Yes, once we define addition with limits as possible, basic forms 7 and 9 are a direct arithmetic consequence of it.

axiomatic?

8: 8.- Limit of the Exponent of a Function.

Limit of [f(x)]^n when x-->a = [Limit of f(x)]^x

Limit of [f(x)]^n when x-->a = [Limit of f(x)]^n

Limit of [f(x)]^n when x-->a = Limit of f(x) * Limit of a^n

Limit of [f(x)]^n when x-->a = Limit of f(x) * Limit of n

9: 10.- Limit of a Composite Function.

Limit of f(g(x)) when x--> a = Limit of f(x) * Limit of g(x)

Limit of f(g(x)) when x--> a = Limit of f(x) / Limit of g(x) when Limit of g(x) ≠0

Limit of f(g(x)) when x--> a = f[limit of g(x)]

Limit of f(g(x)) when x--> a = g[limit of f(x)]

10: What is the process that leads to construct Basic Form #11?

Pythagorean Identity

Squeeze Theorem

Law of sines

Law of Cosines

11: Write down Basic Form #12 five times in a sheet of paper.

Okay, I did it

How is that suppose to help me?