The graph of y = ∫ 0 x l ( t ) d t , where l is a piecewise constant function , is shown here. Over which intervals is l positive? Over which intervals is it negative? Over which intervals, if any, is it equal to zero? Over which intervals is l increasing? Over which is it decreasing? Over which, if any, is it constant? What is the average value of l ?
The graph of y = ∫ 0 x l ( t ) d t , where l is a piecewise constant function , is shown here. Over which intervals is l positive? Over which intervals is it negative? Over which intervals, if any, is it equal to zero? Over which intervals is l increasing? Over which is it decreasing? Over which, if any, is it constant? What is the average value of l ?
The graph of
y
=
∫
0
x
l
(
t
)
d
t
, where
l
is a piecewise constant function, is shown here.
Over which intervals is
l
positive? Over which intervals is it negative? Over which intervals, if any, is it equal to zero?
Over which intervals is
l
increasing? Over which is it decreasing? Over which, if any, is it constant? What is the average value of
l
?
Definition Definition Group of one or more functions defined at different and non-overlapping domains. The rule of a piecewise function is different for different pieces or portions of the domain.
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
=
Q6 What will be the allowable bearing capacity of sand having p = 37° and ydry
19 kN/m³ for (i) 1.5 m strip foundation (ii) 1.5 m x 1.5 m square footing and
(iii)1.5m x 2m rectangular footing. The footings are placed at a depth of 1.5 m
below ground level. Assume F, = 2.5. Use Terzaghi's equations.
0
Ne
Na
Ny
35 57.8 41.4 42.4
40 95.7 81.3 100.4
Q1 The SPT records versus depth are given in table below. Find qan for the raft 12%
foundation with BxB-10x10m and depth of raft D-2m, the allowable
settlement is 50mm.
Elevation, m 0.5 2
2 6.5 9.5 13 18 25
No.of blows, N 11 15 29 32 30 44
0
estigate shear
12%
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Fundamental Theorem of Calculus 1 | Geometric Idea + Chain Rule Example; Author: Dr. Trefor Bazett;https://www.youtube.com/watch?v=hAfpl8jLFOs;License: Standard YouTube License, CC-BY