Limits

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Reminders

If the left-hand limit of a function is not equal to the right-hand limit of the function, then the limit does not exist.

If the highest power of x in a rational expression is in the numerator, then the limit as x approaches infinity is infinity. ex. the limit of x as it approaches infinity (5x^7 - 3x) / (16x^6 - 3x^2) = infinity

If the highest power of x in a rational expression is in the denominator, then the limit as x approaches infinity is zero. ex. the limit of x as it approaches infinity (5x^6 - 3x) / (16x^7 - 3x^2) = 0

If the highest power of x in a rational expression is the same in both the numerator and denominator, then the limit as x approaches infinity is the coefficient of the highest term in the numerator divided by the coefficient of the highest term in the denominator. ex. the limit of x as it approaches infinity (5x^7 - 3x) / (16x^7 - 3x^2) = 5/16

Limits of Trigonometric Functions

the limit of x as it approaches 0 (sinx) / (x) = 1 (x is in radians, not degrees)

the limit of x as it approaches 0 (cosx - 1) / (x) = 0

the limit of x as it approaches 0 (sin ax) / (x) = a

the limit of x as it approaches 0 (sin ax) / (sin bx) = a/b