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If the birth rate of a population is b(t)= − 2200e
0.024t people per year and the death rate
is d(t)= − 1460e
0.018t people per year, find the area between these curves for 0 < t < 10.
What does this area represent? Also plot the curves using MATLAB.
Let F(x)=∫
t−3
t
2+7
for − ∞ < x < ∞
x
(a) Find the value of x where F attains its minimum value.
(b) Find intervals over which F is only increasing or only decreasing.
(c) Find open intervals over which F is only concave up or only concave down.
Determine whether the function f is integrable on the interval [−1,1].
(a) f(x) = cosx
(b) f(x)={
x
|x|
x ≠ 0
0 x = 0
(c) f(x)={
1
x
2
x ≠ 0
0 x = 0
(d) f(x)={
Sin(
1
x
) x ≠ 0
0 x = 0
(a) Evaluate∫[
x
√x
2+1
]dx.
(b) Use MATLAB to generate some typical integral curves of f(x) =
x
√x
2+1
over the
interval (−5,5).
A light hangs 15 feet directly above a straight walk on which man 6 feet tall is walking. How fast (in ft/sec) is the end of the man’s shadow travelling when he is walking away from the light at rate of 3 mile per hour.
Given that R denotes the set of all real numbers Z, the set of all integers, and Z set of all negative integers, describe each of the following:
a. When we cough, the trachea (windpipe) contracts to increase the velocity of the air going out. This raises the questions of how much it should contract to maximize the velocity and whether it really contracts that much when we cough.
Under reasonable assumptions about the elasticity of the tracheal wall and about how the air near the wall is slowed by friction, the average flow velocity y can be modeled by the equation , , where is the rest radius of the trachea in centimeters and is a positive constant whose value depends in part on the length of the trachea. Show that is greatest when that is, when the trachea is about contracted. The remarkable fact is that ray photographs confirm that the trachea contracts about this much during a cough.
b. Take to be and to be and graph over the interval . Compare what you see with the claim that is at a maximum.
this question needs to be done pn matlab. Can anybody do this entire question on matlab and send the graph and graph codes
3. a) Define tangent and normal of a curve with figure. Also find the equation of tangent and normal of the ellipse (x ^ 2)/4 + (y ^ 2)/16 = 1 at the point (- 1, 3) .
b) Explain maximum and minimum value of a function with graphically. Evaluate maximum and minimum value of the function f(x) = x ^ 3 - 3x ^ 2 + 3x + 1
Evaluate "\\intop"x2(1 + 2x3)3dx.
2. Evaluate "\\intop"xe7x dx.
3. Find the volume of the solid of revolution when the curve y = 1 + x2 is revolved around the x-axis on [−2, 2].
Show that the curve with parametric equations
x = sin t and y = sin(t + sin t) for 0 ≤ t ≤ 2π
