If you know that lim f(x) exists at an interior point of a domain interval of f, can you find its value by calculating lim f(x)? Give reasons for your answer. X-C X-C+ Choose the correct answer below. B OA. Yes, because f(x) has a limit as x approaches c if and only if and only if it has left-hand and right-hand limits there and these limits are equal. OB. Yes, because for e > 0, if f(x) = L as x approaches c, then f(x) has a left-hand limit L-e and a right-hand limit L + e. OC. No, because if f(x) has a limit as x approaches c, then the left-hand and right-hand limits do not exist. O D. No, because if f(x) has a limit as x approaches c, the left-hand and right-hand limits may not be equal. VAI

Calculus: Early Transcendentals
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Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
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If you know that lim f(x) exists at an interior point of a domain interval of f, can you find its value by calculating lim f(x)? Give reasons for your answer.
X-C
X→C
Choose the correct answer below.
...
+
A. Yes, because f(x) has a limit as x approaches c if and only if and only if it has left-hand and right-hand limits there and these limits are equal.
B. Yes, because for &> 0, if f(x) = L as x approaches c, then f(x) has a left-hand limit L- & and a right-hand limit L + ε.
C. No, because if f(x) has a limit as x approaches c, then the left-hand and right-hand limits do not exist.
O D. No, because if f(x) has a limit as x approaches c, the left-hand and right-hand limits may not be equal.
Transcribed Image Text:If you know that lim f(x) exists at an interior point of a domain interval of f, can you find its value by calculating lim f(x)? Give reasons for your answer. X-C X→C Choose the correct answer below. ... + A. Yes, because f(x) has a limit as x approaches c if and only if and only if it has left-hand and right-hand limits there and these limits are equal. B. Yes, because for &> 0, if f(x) = L as x approaches c, then f(x) has a left-hand limit L- & and a right-hand limit L + ε. C. No, because if f(x) has a limit as x approaches c, then the left-hand and right-hand limits do not exist. O D. No, because if f(x) has a limit as x approaches c, the left-hand and right-hand limits may not be equal.
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