# Real Analysis

## Quiz by Anitha Cruz PSGRKCW

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- Q1
Let f be a bounded function defined on [a,b] and let P be a partition of [a,b]. If P* is a refinement of P then

L(P*,f) $\backslash le$ L(P*f)

U(P*,f) $\backslash ge$ U(P*f)

L(P*,f) $\backslash ge$ L(P*f)

U(P*,f) $\backslash le$ U(P*f)

30s - Q2
If P

_{1}& P_{2}be any two partitions of [a,b] thenU(P

_{1},f) $=$ L(P_{2},f)U(P

_{1},f) $\backslash le$ L(P_{2},f)U(P

_{1},f) $\backslash ge$ L(P_{2},f)U(P

_{1},f) $\backslash le$ U(P_{2},f)30s - Q330s
- Q430s
- Q5
Let f be real value bounded function defined on [a,b]. Then lower Riemann integral f over [a,b] _____ the upper Riemann integral of f over [a,b]

can exceed

cannot exceed

none

may or maynot exceed

30s