In Exercises 59-70, the domain of each piecewise function is ( − ∞ , ∞ ) a. Graph each function. b. Use your graph to determine the function's range. f ( x ) = { − 1 2 x 2 if x < 1 2 x + 1 if x ≥ 1
In Exercises 59-70, the domain of each piecewise function is ( − ∞ , ∞ ) a. Graph each function. b. Use your graph to determine the function's range. f ( x ) = { − 1 2 x 2 if x < 1 2 x + 1 if x ≥ 1
Solution Summary: The author explains the function f, which is a piecewise function.
In Exercises 59-70, the domain of each piecewise function is
(
−
∞
,
∞
)
a.Graph each function.
b.Use your graph to determine the function's range.
f
(
x
)
=
{
−
1
2
x
2
if
x
<
1
2
x
+
1
if
x
≥
1
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.
The velocity of a particle moves along the x-axis and is given by the equation ds/dt = 40 - 3t^2 m/s. Calculate the acceleration at time t=2 s and t=4 s. Calculate also the total displacement at the given interval. Assume at t=0 s=5m.Write the solution using pen and draw the graph if needed.
The velocity of a particle moves along the x-axis and is given by the equation ds/dt = 40 - 3t^2 m/s. Calculate the acceleration at time t=2 s and t=4 s. Calculate also the total displacement at the given interval. Assume at t=0 s=5m.Write the solution using pen and draw the graph if needed.
4. Use method of separation of variable to solve the following wave equation
მłu
J²u
subject to
u(0,t) =0, for t> 0,
u(л,t) = 0, for t> 0,
=
t> 0,
at²
ax²'
u(x, 0) = 0,
0.01 x,
ut(x, 0) =
Π
0.01 (π-x),
0
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