Sketch by hand the graph of F that satisfies: (a) f(0) is not defined, (b) lim as x approaches 0 from left of f(x) does not exist and (c) lim as x approaches 0 from right f(x)=2. is the function f(x)continuous from the left at x = 0? Is the function f(x) continuous at x=0 from the right? is the function f(x) continuous at x = 0? Explain.

Solution Summary

Limits and continuous functions are investigated. The solution is detailed and well presented. The response was given a rating of "5/5" by the student who originally posted the question.

... not continuous at x =0. This posting explains the concepts of limits and continuity in details by providing four examples of functions. 1. Create a function, f ...

... 12.1 Given Figure 12.1, tell where f is continuous. ... to twelve problems involving functions, continuity, finding ... of a projectile, finding limits, finding limits...

... we can say better-behaved functions as follows ... is better-behaved than continuous function Continuous function is better ... a sequence {xn } has a limit c , then ...

... of n, for f (n) (0) where f is each of the functions (1) sin ... R is differentiable at a point a ∈ R if: a) f is continuous at the point a b) the limit f ( x ...

... can be approximated by a straight-segments function like that ... on page 39 as the set of all functions continuous on interval ... (aA) Suppose is a limit point for ...

... ie the limit does not exist Solution: ( ) It seems that the limit is 0 ... is continuous since it is a product of continuous functions ( ) is continuous...

... what value of k will the function f be continuous on ... lim_(x -1)f(x) (exists, but this limit is not ... The derivatives and continuity of functions are examined. ...