Remember one-sided limits? Well, these are very useful when dealing with piecewise functions. For example, analyze the limit at x=2 of the function that gives (x-2)² for values lower than 2 and 2-x² for values lager than 2.
Limits_of_trigonometric_functions
Find limits of trigonometric functions by manipulating the functions (using trigonometric identities) into expressions that are nicer to handle. For example, find the limit of sin(x)/sin(2x) at x=0.
Removable discontinuities are points where a function isn't continuous but can become continuous with a small adjustment. Analyze such points and determine what adjustments should be made to "remove" them.
Review your limit-evaluation skills with some challenge problems.
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There are some limits that want us to work a little before we find them. Learn about two main methods of dealing with such limits: factorization and rationalization. For example, find the limit of (x²-1)/(x-1) at x=1.
The Squeeze theorem (or Sandwich theorem) states that for any three functions f, g, and h, if f(x)≤g(x)≤h(x) for all x-values on an interval except for a single value x=a, and the limits of f and h at x=a are equal to L, then the limit of g at x=a must be equal to L as well. This may seem simple but it's pure genius. Learn how it helps us find tricky limits like sin(x)/x at x=0.
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Take your first steps in finding limits algebraically. For example, find the limit of x²+5x at x=2, or determine whether the limit of 2x/(x+1) at x=-1 exists.
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