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KonstantinChe [14]
3 years ago
9

Given that f (x )is continuous. f (3 )equals 1, f (1 )equals 6, f (6 )equals negative 2, and f (negative 2 )equals 3. Determine

limit as x rightwards arrow 6 to the power of plus of f (x ), and limit as x rightwards arrow negative 2 to the power of minus of f (x ).
Mathematics
1 answer:
Liono4ka [1.6K]3 years ago
3 0

Given:

f(x) is continuous, f(3)=1,f(1)=6,f(6)=-2,f(-2)=3.

To find:

The value of \lim_{x\to 6^+}f(x) and \lim_{x\to -2^-}f(x).

Solution:

If a function f(x) is continuous at x=c, then

\lim_{x\to c^-}f(x)=f(c)=\lim_{x\to c^+}f(x)

It is given that the function f(x) 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,

\lim_{x\to 6^-}f(x)=f(6)=\lim_{x\to 6^+}f(x)

\lim_{x\to 6^+}f(x)=f(6)

\lim_{x\to 6^+}f(x)=-2

The function is continuous for -2. So,

\lim_{x\to -2^-}f(x)=f(-2)=\lim_{x\to -2^+}f(x)

\lim_{x\to -2^-}f(x)=f(-2)

\lim_{x\to -2^-}f(x)=3

Therefore, \lim_{x\to 6^+}f(x)=-2 and \lim_{x\to -2^-}f(x)=3.

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