# Evaluate the limit? : #lim_(x rarr 0) ( tanx-x ) / (x-sinx) #

# lim_(x rarr 0) ( tanx-x ) / (x-sinx) = 2 #

We want to find:

Method 1 : Graphically graph{( tanx-x ) / (x-sinx) [-8.594, 9.18, -1.39, 7.494]}

Although far from conclusive, it appears that:

Method 2 : L'Hôpital's rule

And so applying L'Hôpital's rule we get:

This limits is also of an indeterminate form, so we can apply L'Hôpital's again to get:

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The limit of (tanx-x)/(x-sinx) as x approaches 0 is 1.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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- How do you find the limit #lim (2x+4)/(5-3x)# as #x->oo#?

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