Use the definition of continuity and the properties of limits to show that the f

Amari Flowers 2021-10-29 Answered
Use the definition of continuity and the properties of limits to show that the function
f(x)=x16x2 is continuous on the interval [-4,4]
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Nathaniel Kramer
Answered 2021-10-30 Author has 78 answers
Consider the given function as
f(x)=x16x2
Definition of continuity
Function is said to be continuous if limxaf(x)=limxa+f(x)=f(a)
Let a point c[4,4] then,
limxcf(x)=limxcx16x2
=c16c2
And
limxc+f(x)=limxc+x16x2
=c16c2
And
f(c)=c16c2
So, limxcf(x)=limxc+f(x)=f(c)
Hence, function is continuous on the given interval [-4,4]
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Jeffrey Jordon
Answered 2022-06-24 Author has 2313 answers

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