Let f ( x ) = x + 5 on the interval [0, 12]. (A) Use the trapezoidal rule to calculate T 3 and T 6 . How good are these approximations to ∫ 0 12 ( x + 5 ) d x ? Explain. (B) Use Simpson’s rule to calculate S 4 and S 6 . How good are these approximations to ∫ 0 12 ( x + 5 ) d x ? Explain.
Let f ( x ) = x + 5 on the interval [0, 12]. (A) Use the trapezoidal rule to calculate T 3 and T 6 . How good are these approximations to ∫ 0 12 ( x + 5 ) d x ? Explain. (B) Use Simpson’s rule to calculate S 4 and S 6 . How good are these approximations to ∫ 0 12 ( x + 5 ) d x ? Explain.
Solution Summary: The author compares the obtained result with the approximation of the integral displaystyle
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Question 3
The angle bisectors of APQR are PZ, QZ, and RZ. They meet at a single point Z.
(In other words, Z is the incenter of APQR.)
Suppose YZ = 22, QZ = 23, mz WPY 38°, and mzXQZ = 54°.
Find the following measures.
Note that the figure is not drawn to scale.
P
W
Z
X
R
Y
mzXQW
WZ
=
=
0
mz XRZ
=
0°
a
C
d
2
1
-1
0
1
2
3
-1
Graph of f'(x)
(5) The graph of f'(x), the derivative of f(x), is shown in the figure above. The line tangent to the graph
of f'(x) at x=0 is vertical and f'(x) is not differentiable at x = 1. Which of the following statements is
true?
(a) f'(x) does not exist at x = 0.
(b) f(x) has a point of inflection at x = 1.
(c) f(x) has a local maximum at x = 0.
(d) f(x) has a local maximum at x = 1.
Chapter 6 Solutions
Calculus for Business, Economics, Life Sciences, and Social Sciences - Boston U.
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Differential Equation | MIT 18.01SC Single Variable Calculus, Fall 2010; Author: MIT OpenCourseWare;https://www.youtube.com/watch?v=HaOHUfymsuk;License: Standard YouTube License, CC-BY