# If limit of #f(x)=2# and #g(x)=3# as #x->c#, what the limit of #f(x)g(x)# as #x->c#?

# lim_(x rarr c) {f(x)g(x)} = 6#

We are given that:

And so by the properties of limits:

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The limit of f(x)g(x) as x approaches c is 6.

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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 prove that the limit of #(x^2 - x) = 0 # as x approaches 1 using the epsilon delta proof?
- How do you find the limit of #sqrt(3+x) - sqrt(3)/x # as x approaches 0?
- How do you determine the limit of #csc x# as x approaches #oo#?

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