- 1.
- Verify the formula

x8
= 8x7 by starting with the definition of derivative and choosing submenu
items such as Expand and Simplify.BITMAPSETAnswer0.2214in0.205in0ina1
- 2.
- Use Newton's method on the function
f (x) = x2 + 1,
starting with x0 = 0.5. What conclusions can you draw?BITMAPSETAnswer0.2214in0.205in0ina2
- 3.
- Find the equation of one
line that is tangent to the graph of
f (x) = x(x - 1)(x - 3)(x - 6)
at two different points.BITMAPSETAnswer0.2214in0.205in0ina3
- 4.
- For 0 < k < 1, the elliptic
integral
E =

dt has no elementary
solution. Use a series expansion of the integrand to estimate E.
BITMAPSETAnswer0.2214in0.205in0ina4
- 5.
- Find all the solutions to
xy = yx for unequal
positive integers x and y.BITMAPSETAnswer0.2214in0.205in0ina5
- 6.
- Blood flowing through an
artery flows fastest at the center of the artery, and slowest near the walls
of the artery where friction is a factor. In fact, the velocity is given by
the formula
v(r) = α(R2 - r2), where α is a constant, R
is the radius of the artery, and r is the distance from the center.
Set up an integral that gives the total blood flow through an artery. Show
that, if an artery is constricted to one-half of its original radius, the
blood flow (assuming constant blood pressure) is reduced to
of its original flow.BITMAPSETAnswer0.2214in0.205in0ina6
- 7.
- The mass of an object traveling at a velocity v with
rest mass m0 is given by
where c is the speed of light. Use a Maclaurin series expansion to show
the increase in mass at low velocities.BITMAPSETAnswer0.2214in0.205in0ina7
- 8.
- Evaluate
2xcos bxdx and simplify the
answer.BITMAPSETAnswer0.2214in0.205in0ina8
- 9.
- Evaluate

dx .BITMAPSETAnswer0.2214in0.205in0ina9
- 10.
- Evaluate

sin(x1+h) dx .BITMAPSETAnswer0.2214in0.205in0ina10
- 11.
- The Fundamental Theorem of
Calculus says that if f is continuous on a closed interval
a, b
, then
- a.
- If g is defined by
g(x) =
f (t)dt for
x∈
a, b
, then
g′(x) = f (x), and
- b.
- If F is any antiderivative of f, then.
f (x)dx = F(b) - F(a).
Demonstrate that these two conditions hold for each of the three functions
f (x) = x3,
f (x) = xex, and
f (x) = sin2x cos x.BITMAPSETAnswer0.2214in0.205in0ina11