... if the lim xàa f (x) cannot be directly calculated, but we are able to find two functions, g and h, that have the same limit L as xàa and such that f is "pinched" between g and h by means of the inequalities g (x) W f (x) W h (x). It is clear that f (x) must also approach L as xàa because the graph of f lies between the graphs of g and h. Thus, the lim xàa g (x) = lim xà ...   h (x) = L, since g and h have the same limit as x approaches a. The pinching theorem has applications to continually used limits of trigonometric functions; a) lim xà0 sin x = 0; lim xà0 cos x =...

• Word Count: 2379
• Approx Pages: 10
• Grade Level: High School

... , we already know about the rule of left and right hand limits so we"re one third of the way there. 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. This causes the left and right hand limits to not be equal therefore causing the limit to not ... . Finally, the last reason for a limit to not exist would be for the function to wiggle from one point to the next, never reaching a single numeric value. This occurs with trigonometric functions. There are many ways to solve for limits. In the next few paragraphs, we will...

• Word Count: 614
• Approx Pages: 2
• Grade Level: High School