Calc 1 - Exam 1 Definitions

Formal Definition of Limit

if for any ε > 0, there exists a corresponding δ > 0 such that |f(x) - L| < ε. whenever 0 < |x - c| < δ

Continuity of a Function at a Point

we say that a function f(x) is continuous at c if lim x→c f(x) = f(c)

Vertical Asymptote

if lim x→c+ f(x) = ±∞ or lim x→c- f(x) = ±∞, then we call x=c a vertical asymptote for f(x)

Horizontal Asymptote

if lim x→±∞ f(x) = L, then we call L a horizontal asymptote for f(x)

The Squeeze Theorem

if f(x) < g(x) < h(x) for all x, and lim x→c f(x) - lim x→c h(x) = L, then lim x→c g(x) = L

Intermediate Value Theorem

If f is a continuous function on the interval from a to b and f(a) ≠ f(b), then for any value N between f(a) and f(b), there exists a z in the interval such that f(z) = N

Special Limit for Sin

lim θ→0 (sinθ)/θ = 1

Special Limit for Cosine

lim θ→0 [(cosθ)-1]/θ = 0