Given that
limx→cf(x)=43
limx→cg(x)=12
limx→ch(x)=−3
We can use these values in the following examples to understand some of the limit theorems.
limit theorems.
Ex 1. limx→cf(x)±limx→cg(x)
To find limx→cf(x)±limx→cg(x) , we use the given values,
limx→cf(x)=43 and limx→cg(x)=12
Therefore,
=43±(12)
=43+(12)=451 and =43−(12)=4−45
Ex 2. limx→c[(2.f(x))+12.g(x)]
To find limx→c[(2.f(x))+12.g(x)] , we use the given values,
limx→c[(2.f(x))+12.g(x)]=[(2.limx→cf(x))+12.limx→cg(x)]
=[(2.34)+(12)(12)]
=38+12=344
limx→cf(x)=43 and limx→cg(x)=12
Therefore,
=2(43)+(12)=227
Ex 3. limx→c42h(x)f(x)−g(x)
=limx→c2h(x)limx→c4f(x)−limx→cg(x)
=2limx→ch(x)4limx→cf(x)−limx→cg(x)
=(2)(−3)4(43)−(12)
=23
Ex 4. limx→c[h(x)−4f(x)]
=limx→ch(x)−4limx→cf(x)
=(−3)−4(43)
=−3−3
=−6
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