Investigation Consider the function f ( x ) = 2 x n x 4 + 1 for nonnegative integer values of n . (a) Discuss the relationship between the value of n and the symmetry of the graph. (b) For which values of n will the x-axis be the horizontal asymptote? (c) For which value of n will y = 2 be the horizontal asymptote? (d) What is the asymptote of the graph when y = 2 (e) Use a graphing utility to graph f for the indicated values of n in the table. Use the graph to determine the number of extrema M and the number of inflection points N of the graph. n 0 1 2 3 4 5 M N
Investigation Consider the function f ( x ) = 2 x n x 4 + 1 for nonnegative integer values of n . (a) Discuss the relationship between the value of n and the symmetry of the graph. (b) For which values of n will the x-axis be the horizontal asymptote? (c) For which value of n will y = 2 be the horizontal asymptote? (d) What is the asymptote of the graph when y = 2 (e) Use a graphing utility to graph f for the indicated values of n in the table. Use the graph to determine the number of extrema M and the number of inflection points N of the graph. n 0 1 2 3 4 5 M N
Solution Summary: The author explains how to determine the relation between the symmetry of the function f(x) and the value of n.
(a) Discuss the relationship between the value of n and the symmetry of the graph.
(b) For which values of n will the x-axis be the horizontal asymptote?
(c) For which value of n will
y
=
2
be the horizontal asymptote?
(d) What is the asymptote of the graph when
y
=
2
(e) Use a graphing utility to graph f for the indicated values of n in the table. Use the graph to determine the number of extrema M and the number of inflection points N of the graph.
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rmine the immediate settlement for points A and B shown in
figure below knowing that Aq,-200kN/m², E-20000kN/m², u=0.5, Depth
of foundation (DF-0), thickness of layer below footing (H)=20m.
4m
B
2m
2m
A
2m
+
2m
4m
sy = f(x)
+
+
+
+
+
+
+
+
+
X
3
4
5
7
8
9
The function of shown in the figure is continuous on the closed interval [0, 9] and differentiable on the open
interval (0, 9). Which of the following points satisfies conclusions of both the Intermediate Value Theorem
and the Mean Value Theorem for f on the closed interval [0, 9] ?
(A
A
B
B
C
D
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