# What is the limit as x approaches 0 of #(1-cos(x))/sin(x)#?

The limit is

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The limit as x approaches 0 of (1-cos(x))/sin(x) is 0.

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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.

- What is the limit of #( 1/(x-1) - 2/(x^2-1) )# as x approaches 1?
- What is the limit of lnx-ln(pi)/x-(pi) when x approaches to (pi) from left?
- What is the limit of #(sqrt (9x^6 - x) ) / (x^3 + 4)# as x approaches negative infinity?
- What is the limit of #Abs(sinx) # as x approaches infinity?
- How do you find #lim (x^2-x+4)/(3x^2+2x-3)# as #x->oo#?

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