Limits of a Piecewise Function In Exercises 33 and 34, sketch the graph of f . Then identify the values of c for which lim x → c f ( x ) exists. f ( x ) = { sin x , x < 2 1 − cos x , 0 ≤ x ≤ π cos x , x < π
Limits of a Piecewise Function In Exercises 33 and 34, sketch the graph of f . Then identify the values of c for which lim x → c f ( x ) exists. f ( x ) = { sin x , x < 2 1 − cos x , 0 ≤ x ≤ π cos x , x < π
Limits of a Piecewise Function In Exercises 33 and 34, sketch the graph of f. Then identify the values of c for which
lim
x
→
c
f
(
x
)
exists.
f
(
x
)
=
{
sin
x
,
x
<
2
1
−
cos
x
,
0
≤
x
≤
π
cos
x
,
x
<
π
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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