# Find the required limit algebrically, if it exists. lim (x+3)/(x-3) if x approaches 4 ?

The limit exists and is equal to 7

I am not sure exactly what is meant by "algebraically" in the question. So I will try to show this by a couple of different approaches.

Method 1

Method 2

Now

if we choose

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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.

- How do you find the limit of #cosx# as x approaches infinity?
- How do you find the limit of #e^(1/x)# as x approaches #0^-#?
- How do you find the limit of #(1-cos(4x))/(1-cos(3x)# as x approaches 0?
- How do you find the limit of #(tan^3 (2x))/ x^3# as x approaches 0?
- How do you find #lim 1+1/x# as #x->0^+#?

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