A function f defined on a closed interval [a, b] is said to be continu

1.	A function f defined on a closed interval [a, b] is said to be continuous at the end point if1. it is continuous at the right at 'a'2. it is discontinuous at the right at 'a'3. the value of 'a' is zero4. f(a) = f(b)
Answer» Correct Answer - Option 1 : it is continuous at the right at 'a' Concept: Continuity at an endpoint- A function f defined on a closed interval [a, b] is said to be continuous at the endpoint 'a' if it is continuous from the right at a, i.e, ⇒ \(% MathType!MTEF!2!1!+- % feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaCbeaeaaqa % aaaaaaaaWdbiGacYgacaGGPbGaaiyBaaWcpaqaa8qacaWG4bGaeyOK % H4QaamyyaiabgUcaRiaaicdaa8aabeaak8qacaWGMbWaaeWaa8aaba % WdbiaadIhaaiaawIcacaGLPaaacqGH9aqpcaWGMbWaaeWaa8aabaWd % biaadggaaiaawIcacaGLPaaaaaa!46E3! \mathop {\lim }\limits_{x \to a + 0} f\left( x \right) = f\left( a \right)\) Also, the function is continuous at the endpoint b of [a, b] if, ⇒ \(% MathType!MTEF!2!1!+- % feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaCbeaeaaqa % aaaaaaaaWdbiGacYgacaGGPbGaaiyBaaWcpaqaa8qacaWG4bGaeyOK % H4QaamOyaiabgkHiTiaaicdaa8aabeaak8qacaWGMbWaaeWaa8aaba % WdbiaadIhaaiaawIcacaGLPaaacqGH9aqpcaWGMbWaaeWaa8aabaWd % biaadkgaaiaawIcacaGLPaaaaaa!46F0! \mathop {\lim }\limits_{x \to b - 0} f\left( x \right) = f\left( b \right)\)

A function f defined on a closed interval [a, b] is said to be continuous at the end point if1. it is continuous at the right at 'a'2. it is discontinuous at the right at 'a'3. the value of 'a' is zero4. f(a) = f(b)

Answer» Correct Answer - Option 1 : it is continuous at the right at 'a'

Concept:

Continuity at an endpoint-

A function f defined on a closed interval [a, b] is said to be continuous at the endpoint 'a' if it is continuous from the right at a, i.e,

⇒ \(% MathType!MTEF!2!1!+- % feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaCbeaeaaqa % aaaaaaaaWdbiGacYgacaGGPbGaaiyBaaWcpaqaa8qacaWG4bGaeyOK % H4QaamyyaiabgUcaRiaaicdaa8aabeaak8qacaWGMbWaaeWaa8aaba % WdbiaadIhaaiaawIcacaGLPaaacqGH9aqpcaWGMbWaaeWaa8aabaWd % biaadggaaiaawIcacaGLPaaaaaa!46E3! \mathop {\lim }\limits_{x \to a + 0} f\left( x \right) = f\left( a \right)\)

Also, the function is continuous at the endpoint b of [a, b] if,

⇒ \(% MathType!MTEF!2!1!+- % feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaCbeaeaaqa % aaaaaaaaWdbiGacYgacaGGPbGaaiyBaaWcpaqaa8qacaWG4bGaeyOK % H4QaamOyaiabgkHiTiaaicdaa8aabeaak8qacaWGMbWaaeWaa8aaba % WdbiaadIhaaiaawIcacaGLPaaacqGH9aqpcaWGMbWaaeWaa8aabaWd % biaadkgaaiaawIcacaGLPaaaaaa!46F0! \mathop {\lim }\limits_{x \to b - 0} f\left( x \right) = f\left( b \right)\)

A function f defined on a closed interval [a, b] is said to be continuous at the end point if1. it is continuous at the right at 'a'2. it is discontinuous at the right at 'a'3. the value of 'a' is zero4. f(a) = f(b)

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