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Real Analysis

Quiz by Anitha Cruz PSGRKCW

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Q 1/5
Score 0
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
29
L(P*,f) $\le$ L(P*f)
U(P*,f) $\ge$ U(P*f)
L(P*,f) $\ge$ L(P*f)
U(P*,f) $\le$ U(P*f)

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5 questions

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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) $\le$ L(P*f)
U(P*,f) $\ge$ U(P*f)
L(P*,f) $\ge$ L(P*f)
U(P*,f) $\le$ U(P*f)
30s
Q2
If P₁ & P₂ be any two partitions of [a,b] then
U(P₁,f) $=$ L(P₂,f)
U(P₁,f) $\le$ L(P₂,f)
U(P₁,f) $\ge$ L(P₂,f)
U(P₁,f) $\le$ U(P₂,f)
30s
Q3
30s
Q4
30s
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

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