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If limit of #f(x)=3/2# and #g(x)=1/2# as #x->c#, what the limit of #f(x)g(x)# as #x->c#?

Answer 1

Paisley Johnson

# lim_(xrarrc) {f(x)g(x)} =3/4#

This is one of the basic properties of limits: # lim_(xrarrc) {f(x)g(x)} = {lim_(xrarrc)f(x)}{ lim_(xrarrc) g(x) }#

We are told that: #lim_(xrarrc)f(x)=3/2#; and #lim_(xrarrc) g(x) =1/2#

Hence, # lim_(xrarrc) {f(x)g(x)} = 3/2*1/2=3/4#

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Answer 2

Samantha Adkison

The limit of f(x)g(x) as x approaches c is 3/4.

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Answer from HIX Tutor

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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If limit of #f(x)=3/2# and #g(x)=1/2# as #x-&gt;c#, what the limit of #f(x)g(x)# as #x-&gt;c#?

If limit of #f(x)=3/2# and #g(x)=1/2# as #x->c#, what the limit of #f(x)g(x)# as #x->c#?