f (x) 1 -3 -7 -9 continuous function f is decreasing for all æ. Selected values of f are given in the table above, where a is a constant with 0 < a < 3. Let R be the right Riemann sum approximation for f (x) dz using the four subintervals indicated by the data in the table. Which of the following statements is true? R= (a² – 0) · 1+ (3a – a²) · (-1)+(6a – 3a) · (-3)+(7a – 6a) · (-7) and is an underestimate for | f(2) dz. A R= (a² – 0) · 1+ (3a – a²) · (-1)+(6a – 3a) · (-3)+ (7a – 6a) · (-7) and is an overestimate for | (2) dz. B R= (a² – 0) · (-1)+(3a – a²)·(-3)+(6a – 3a) · (-7)+(7a – 6a) · (-9) and is an underestimate for | f(2) dz. R= (a² – 0) · (-1)+(3a – a²)·(-3)+(6a – 3a) · (-7)+(7a – 6a) · (-9) and is an overestimate for f (x) dz. D

f (x) 1 -3 -7 -9 continuous function f is decreasing for all æ. Selected values of f are given in the table above, where a is a constant with 0 < a < 3. Let R be the right Riemann sum approximation for f (x) dz using the four subintervals indicated by the data in the table. Which of the following statements is true? R= (a² – 0) · 1+ (3a – a²) · (-1)+(6a – 3a) · (-3)+(7a – 6a) · (-7) and is an underestimate for | f(2) dz. A R= (a² – 0) · 1+ (3a – a²) · (-1)+(6a – 3a) · (-3)+ (7a – 6a) · (-7) and is an overestimate for | (2) dz. B R= (a² – 0) · (-1)+(3a – a²)·(-3)+(6a – 3a) · (-7)+(7a – 6a) · (-9) and is an underestimate for | f(2) dz. R= (a² – 0) · (-1)+(3a – a²)·(-3)+(6a – 3a) · (-7)+(7a – 6a) · (-9) and is an overestimate for f (x) dz. D

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Concept explainers

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as:

Question

2
За
ба
7a
f (x)
1
-1
-3
-7
-9
The continuous function f is decreasing for all r. Selected values of f are given in the table above, where a is a constant with 0 < a << 3. Let Rbe the right Riemann sum approximation for
7a
| f (x) da using the four subintervals indicated by the data in the table. Which of the following statements is true?
A
R3 (а? — 0) . 1+ (За — а?) (-1) + (6а — За) - (-3) + (7а - 6а) - (-7) and is an underestimate for
f (x) dr.
7a
R 3 (а? — 0) . 1+ (За — а?) . (-1) + (ба — За) . (-3) + (7а — 6а) . (-7) and is an overestimate for
f (2) da.
B
R = (a² – 0) · (-1)+ (3a – a²) · (-3)+ (6a – 3a) · (-7) + (7a – 6a) · (-9) and is an underestimate for
f(2) da.
R 3 (a? — 0) . (-1) + (За — а?) . (-3) + (ба — За) . (-7) + (7a — 6а) - (-9) and is an overestimate for
f (x) dz.
D

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