Another reason for a limit wouldn"t exist would be for a graph to break, if the pieces don"t meet up at an intended height. ... Another reason would occur if a function increases or decreases indefinitely at a given x-value (Stewart 61). This occurs when a function has a vertical asymptote at x=a causing the function to increase or decrease indefinitely. ... This occurs with trigonometric functions. ... A Horizontal Asymptote is the height that a function tries to, but cannot, reach as the function's x-values get infinitely large or small. ...

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