Unit 1: Limits and Continuity

Lim x->a (1/ x-a)

+/- oo and DNE with a vertical asymptote at x=a

lim x->0 (cosx-1/x)

0

If n<m, lim x->oo (ax^n/bx^m)

0 with a horizontal asymptote at y=0 (BOBO)

Lim x-> 0 (e^x -1/x)

1

lim x->0 (sinx/x)

1

F(x) is continuous at x=a if

A. Lim x->a f(x) exists B. F(a) existed C. Lim x->a f(x) = f(a)

If n=m, lim x->oo (ax^n/bx^m)

A/b with a horizontal asymptote at y= a/b (BETC)

Lim x->0 (1/x)

DNE

Lim x->0 (IxI/x)

DNE

Intermediate Value Theorem

If f is a continuous function on the interval [a,b], then there exists a c where a<c<b such that f(a) <f(c) > f(b).?

Squeeze Theorem

If f, g, and h are defined functions, f(x) _< g(x) _< h(x) for all x, and lim x->a f(x) = lim x->a h(x) = L, then: lim x-> a g(x) = L

Lim x->a f(x) exists

If lim x->a- f(x) = lim x->a+ f(x)

Lim x-> a (x(x-a)/ x-a)

Lim x->a x=a with a hole in the graph at x=a

Lim x->0 (1/x^2)

oo

If n>m, lim x->oo (ax^n/bx^m)

oo and the limit DNE (BOTU)