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Sagot :
Given:
[tex]f(x)[/tex] is continuous, [tex]f(3)=1,f(1)=6,f(6)=-2,f(-2)=3[/tex].
To find:
The value of [tex]\lim_{x\to 6^+}f(x)[/tex] and [tex]\lim_{x\to -2^-}f(x)[/tex].
Solution:
If a function f(x) is continuous at [tex]x=c[/tex], then
[tex]\lim_{x\to c^-}f(x)=f(c)=\lim_{x\to c^+}f(x)[/tex]
It is given that the function [tex]f(x)[/tex] is continuous. It means it is continuous for each value and the left-hand and right-hand limits are equal to the value of the function.
The function is continuous for 6. So,
[tex]\lim_{x\to 6^-}f(x)=f(6)=\lim_{x\to 6^+}f(x)[/tex]
[tex]\lim_{x\to 6^+}f(x)=f(6)[/tex]
[tex]\lim_{x\to 6^+}f(x)=-2[/tex]
The function is continuous for -2. So,
[tex]\lim_{x\to -2^-}f(x)=f(-2)=\lim_{x\to -2^+}f(x)[/tex]
[tex]\lim_{x\to -2^-}f(x)=f(-2)[/tex]
[tex]\lim_{x\to -2^-}f(x)=3[/tex]
Therefore, [tex]\lim_{x\to 6^+}f(x)=-2[/tex] and [tex]\lim_{x\to -2^-}f(x)=3[/tex].
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