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Recall that in general if we have a limit of the following form where both...

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Calculus

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Recall that in general if we have a limit of the following form where both f x 0 and g x 0 then the limit may or may not exist and is called an indeterminate form of type 0 0 We note that this type of limit can be evaluated for certain functions by dividing numerator and denominator by the highest power of x that occurs in the denominator However we are give the following limit where this method does not work f x lim x a g x f x lim x10 For the evaluation of indeterminate forms of type ew where other methods do not work we use L Hospital s Rule This rule states that if f and g are differentiable and g x 0 on an open interval I that contains a except possibly at a where lim f x 0 and lim g x 0 then the following holds as long as the limit on the right side exists or is or x a x a g x cos x 1 x 4x4 We can apply L Hospital s Rule for the given function using a 0 f x cos x 1 1x f x lim lim x a g x x a g x 16x x and g x 4x4 We need to first find both f x and g x

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