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DIA [1.3K]
4 years ago
8

True or False? Picture provided below

Mathematics
1 answer:
OLEGan [10]4 years ago
7 0

Answer:

The statement is true

Step-by-step explanation:

To answer this question we must take the limit of f(x) when the function tends to 1. We must take this limit by the right and the left of 0. (-1 ^{+}; -1 ^{-}). If any of these limits tends to infinity then the function is discontinuous at x = -1.

But if the

\lim_{x \to \\-1^+}f(x)=\lim_{x \to \\-1^-}f(x) = b      <em>Where b is a real number</em>

Then the function is continuous at x = -1

Then.

\lim_{x \to \\-1^+}f(x) = \lim_{x \to \\-1^+}-2x +1\\\\\lim_{x \to \\-1^+}-2(-1) +1 = 3

and

\lim_{x \to \\-1^-}f(x) = \lim_{x \to \\-1^-} 2x+5\\\\\lim_{x \to \\-1^-} 2(-1)+5 = 3

Then:

\lim_{x \to \\-1^+}f(x) = \lim_{x \to \\-1^-}f(x) = 3

Therefore the function is continuous at x = -1. The statement is true

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