Please bear with MathPeer, as we are a brand new site that was created on Sunday, June 03, 2007, and we are still in the development process. The site currently has a few active pages, but the member based features arn't expected to be fully functional until the late June. We expect the site to be in its fully functional stage prior to the start of the next school year.

Limits and Continuity

This page is meant to serve as a quick overview of limits and continuity.

Limit

f has a limit L as x approaches c. Lim xc f(x) = L
Limit of any constant is a constant lim(x) ⇒ c(k) = k
Sum Rule lim(x) ⇒ c(x + 6) = lim x ⇌ c(x) + lim (x) ⇌ c(6) = c + 6
Difference Rule lim(x) ⇒ c(x - 6) = lim x ⇌ c(x) - lim (x) ⇌ c(6) = c - 6
Constant Multiple Rule lim(x) ⇒ c(5*x) = 5*lim x ⇌ c(x) = 5*c

Some limits can have a limit only from one side. lim(x) ⇒ c+ denotes from the right and lim(x) ⇒ c- denotes from the left.

Horizontal Asymptote

y = b is a horizontal asymptote if lim x ⇒ ∞ + = b or lim x ⇒ ∞ - = b
For Horizontal Asymptote's if degree on bottom is less than degree on bottom is less than degree on top, the Horizontal Aysmptote is y=0. Bottome and Top are the same (3 x2/x2)the Horizontal Aysmptote is the leading coefficients (3). Degree on top is higher than bottom then the asymptote is obligue.

Verticle Asymptote

x = a is a verticle asymptote if lim x ⇒ a + = + or - ∞ or lim x ⇒ ∞ - = b
For Horizontal Asymptote's if degree on bottom is less than degree on bottom is less than degree on top, the Horizontal Aysmptote is y=0. Bottome and Top are the same (3 x2/x2)the Horizontal Aysmptote is the leading coefficients (3). Degree on top is higher than bottom then the asymptote is obligue.

Continuity

A point is continuous at a point if it's in the domain if lim x ⇒ c f(x)=f(c), if f(c) is defined, and the limit exists.

Types of Discontinuity

Discontinuities are either removable or non-removable, and there are three types. Jump, infinite, and oscillating.

Function Valuse of Special Angles
Removable Discontinuity
Jump Discontinuity Infinite Discontinuity Oscillating Discontinuity

A continuous function is a function that is continuous at every point.

IROC-lim h ⇒ 0 (f(a+h)-f(a/h))

A normal line to a curve at a poin is the line perpendicular to the tangent at that point.