Math- limits definitions

limits

limit statement

the limit of f(x) as x approaches c equals b

Limit

behavior of a function as you approach a given x-value. (NOT THE SAME AS WHAT IS HAPPENING AT THE X-VALUE)

One sided limit

behavior of a function coming from the left or right side of x-value (two sided limit exists only if the one sided limits are equal)

Cases where limit doesn’t exist

One sided limits not equal, approaches infinity, or oscillation

Definition of continuity

A function is continuous when f(x) is equal to the limit of f(x) as x approaches any number

Guaranteeing Continuity at a point

f(c)= lim x→c f(x)=b

Point discontinuity

limit exists but limit doesn’t equal value of function

Jump discontinuity

One sided limits exist but are not equal to each other

Infinite discontinuity

Outputs are unbounded (limits are equal to infinity)

Continuous function

Continuous at every point of its domain