A) Using a calculus approach, sketch p(x) = -3*x^2 –
300x – 140.
B) What is...
A) Using a calculus approach, sketch p(x) = -3*x^2 –
300x – 140.
B) What is the largest rectangle that can be inscribed inside the
curve, if two of its sides are on the x-axis and the other two lie
on the positive portion of the curve.
Use the techniques of Chapter 4 to sketch the graph of y=
x^4/4+x^3/3-x^2.
a) domain,
b) y-intercept,
c) asymptote(s),
d) intervals of increase and/or decrease,
e) local maximum(s) and/or local minimum(s),
f) intervals of concavity,
g) points of inflection. (For full credit, remember to show all
work and include sign charts for the Increasing/Decreasing and 2nd
Derivative tests.)
Considerapopulationwhoseprobabilitiesaregivenby
p(1)=p(2)=p(3)= 1 3
(a) DetermineE[X]. (b) DetermineSD(X).
σ2σ n =√n
SD(X)=
In the preceding formula, σ is the population standard
deviation, and n is the
(c) Let X denote the sample mean of a sample of size 2 from
this population. Determine the possible values of X along with
their probabilities.
(d) Usetheresultofpart(c)tocomputeE[X]andSD(X).
(e) Areyouranswersconsistent?
Sketch the graph of the given function. (x^2+x-2) / x^2
Give
a) x intercept
b) y intercept
c) Vertical asymtope
d)Horizontal asymtope
e) first derivative
f)second derivative
g)critical numbers
h)extrema max/min
i) y coordinate of exterma
j) possible point of infletion
h)y coordinate of possible point of inflection
k) table
l)graph
Multivariable calculus
Evaluate: ∮ 3? 2 ?? + 2???? using two different methods. C is
the boundary of the graphs C y = x2 from (3, 9) to (0, 0) followed
by the line segment from (0, 0) to (3, 9).
2. Evaluate: ∮(8? − ? 2 ) ?? + [2? − 3? 2 + ?]?? using one
method. C is the boundary of the graph of a circle of radius 4
oriented counterclockwise
Find the following probabilities
a. P(X = 2) when X ∼
Bin(4,0.6)
b. P(X > 2) when X ∼
Bin(8, 0.5)
c. P(X ≤ 2) when X ∼ Bin(5,
0.5)
d. P(3 ≤ X ≤ 5) when X ∼
Bin(6, 0.3)
Suppose X ~ N(6, 3^2).
a. Compute P(X > 9.9)
b. Determine the 95th percentile of X, that is, the constant c
such that P(X < c)= 0.95
c. Find the mean and variance of
Y = 2X -1