# Evaluate the limit? : # lim_(x rarr oo)(3x+1)/(|x|+2) #

graph{(3x+1)/(|x|+2) [-5, 20, -3.5, 3.5]}

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The limit of (3x+1)/(|x|+2) as x approaches infinity is 3.

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

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