Left-Side and Right-Side Continuous

Related BrainMass Solutions

• Proving an Integral Equation

  Suppose a=0,b=1,c=1, and f(x)=x^2, then right hand side is and left hand side is They are the same. An integral equaion is proven. Diagrams are included. The solution is detailed and well presented.

• Limits and Continuous Functions

  146232 Limits and Continuous Functions 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

• Determine all points x at which f is differentiable.

  Therefore, we should check the differentiability only at x =0 Right hand side differentiation: f'(0+) = Lt(h->0) {f(0+h) - f(0)}/h = Lt(h->0) {0 - 0*|0|}/h = Lt(h->0) 0/h = 0 Left Hand side diffentiation: f'(0-) = Lt(h->0) {f(0-h) - f(0)}

• Integration : Fubini's Theorem

  Left Hand side: (*) Right Hand side: (**) Proof: Without loss of generality, we can assume that and f: . Then if , i.e., , then by (a), there is δ>0 so that for all ).

• Function discontinuous at all integers and continuous everywhere

  For each integer n, we have f(n)=n, but for any small positive 1>e>0, we have f(n-e)=n-1 and f(n+e)=n. So at each integer point n, f is continuous on the right side but discontinuous on the left side. The graph of f(x) is in the attachment.

• Real Analysis : Integrability

  side of xk-1 so that the mesh on that side is less than ', and by adding points on the right side of xk+N+1 so that the mesh there is less than ''.

• Continuous Improvement

  So review your SLP's, cases; problems that you addressed(247596, 252008, 252307 & 252475) and for each question on the left side of the table, answer yes or no and list appropriate actions for improvement on the right side.

• Recursion in C++

  "else" branch in drawFourLines() changed as follows: drawFourLines(side/3,level-1); left (90); drawFourLines(side/3,level-1); right(90); drawFourLines(side/3,level-1); right(90); drawFourLines

• Correct use of a Protractor while measuring angles.

  Usually, the bottom scale starts with zero on the right edge and increases to the left ending with 180 degrees on the leftmost edge.