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MATH 1502 Chapter Notes - Chapter 1: Indeterminate Form, Antiderivative, Quotient Rule

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pearcrocodile814

9 Sep 2013

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Indeterminate form meaningless expression that describes the behavior of a function near a point or as it approaches infinity. Ex) 0/0, / , 0 * , - , 0^0, 1^ , ^0. L"hopital"s rule: suppose f(a) = g(a) = 0 and f, g are differentiable on an open interval containing a. Suppose g"(x) is not equal to 0 on this interval (x is not equal to a) Then lim x a f(x)/g(x) = lim x a f"(x)/g"(x) Remarks: differentiate numerator and denominator separately(not quotient rule) 2)keep applying the rule as long as 0/0 remains. 3)be smart ex lim x 0 = x^2/x = lim x 0 2x/1 = 0. Ex lim x 0+ (zero from the right) x-sin(x)/x^3 = lim x 0+ 1-cos(x) =lim x 0+ Sin(x)/6x = lim x-> 0+ -cos(x)/6 = 1/6. L"hopital"s rule works the same for / as it does for 0/0.

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