What are the 8 limit theorems of differential calculus?

Answer 1

Direct Substitution Th.

Limf(x)=f(a)

Theorem 2

If f(x)<g(x), then limf(x)<limg(x)

Squeeze Theorem

If f(x)<g(x)<h(x)

limf(x)=limh(x)=L, then

limg(x)=L

Eps - Delta Definition

if 0<|x-a|<d, then |f(x)-L|<Eps.

Deffinition

fuction is cont. if limf(x)=f(a)

Theorem 5

Any polinomial and rational functions are cont.

Theorem 7

Any pol, ration, root, trig, invers, exponent,

and log functions are continuous.

Theorem 8

limf(g(x))=f(limg(x))

Intermidiate Value Theorem

If f is cont. [a,b] and N is between

f(a) & f(b), then there is a C between

a & b, such that f(C)=N

Deriviative

f'(a)=lim(h->0):{f(a+h)-f(a)}/h

Rate of change

R=lim(x2->x1):{f(x2)-f(x1)}/x2-x1