Use the method of undetermined coefficients to find one solution of
y′′+4y′−3y=(−7x2+7x+7)e4x.
In: Math
1. Differentiate the following functions
A. y=ln(x+sqrt(x^2 -1))
B. y=ln(sinx)
C. y=xlnx-x
D. y=e^x(sinx)
In: Math
Series Solutions of Ordinary Differential Equations For the following problems solve the given differential equation by means of a power series about the given point x0. Find the recurrence relation; also find the first four terms in each of two linearly independent solutions (unless the series terminates sooner). If possible, find the general term in each solution.
(1-x)y"+xy-y=0, x0=0
In: Math
Find the center of mass of a thin plate of constant density
deltaδ
covering the region between the curve
y equals 5 secant squared xy=5sec2x,
negative StartFraction pi Over 6 EndFraction less than or equals x less than or equals StartFraction pi Over 6 EndFraction−π6≤x≤π6
and the x-axis.
In: Math
1. Denote I = ∫10 (1/(1+4x2)) dx
a. Find the exact value of I (for example, by finding an antiderivative of the integrand).
b. For a generic positive integer n, we partition the interval [0, 1] into n equal subintervals [x0, x1], [x1, x2], . . . , [xn-1, xn]. Denote by Ln, Rn, Mn, Tn the Riemann sums corresponding to left-point, right-point, midpoint and trapezoid rule. Use sigma notation to write a formula for each Ln, Rn, Mn, Tn.
c. With the help of your calculator, compute L4, R4, M4, T4. Which of them is closest to I ?
d. Write Matlab codes to compute Ln, Rn, Mn, Tn when n = 8, 16, 32, 64.
e. Denote by en(L) = | Ln − I | the error term from left-point rule. We use similar notations for en(R) , en(M) , en(T) . It is known that en(L) , en(R) ≤ (K(b − a)2)/2n , en(M) ≤ (K~(b − a)3)/24n2 , en(T) ≤ (K~(b − a)3)/12n2 where K = max[a,b] |f'(x)| and K˜ = max[a,b] |f''(x)|. Find n such that the left-point rule gives an error not exceeding e = 0.0001. The same question for the right-point, midpoint, trapezoid rule. Hint: you don’t need to find the exact values of K and K˜ . An upper bound for each of them would be sufficient for this problem.
Need help on e
In: Math
1:
Given that f(4) = 6 and f'(x) = 2/x2+9 for all x.
a) Use a linear approximation or differentials to estimate f(4.04)
b) Is your estimate in part (a) too large or too small? Explain.
2:
a) Given f(x) = (x + 3)sinx, find f'(π) using logarithmic differentiation.
b) Find the value of h'(0) if h(x)+xsin(h(x))= x2+4x-π/2
In: Math
Solve the following using a generating function:
Elizabeth is hosting a party inviting 7 friends. She bought gifts as the following: 8 teddy bears, 8 books, 5 watches. If she wants to give 16 gifts in total, where each person gets two gifts, with at least 2 teddy bears and 1 book. How many possible ways are there to choose from what she bought? Note: Don't distinguish between who gets what, just consider the 16 gifts.
Please only use a generating function, will upvote for that.
In: Math
The estimated monthly sales of Mona Lisa paint-by-number sets is given by the formula q = 105ep − 3p2/2,
where q is the demand in monthly sales and p is the retail price in yen.
(a) Determine the price elasticity of demand E when the
retail price is set at 4 yen.
E =
Interpret your answer.
The demand is going ? up down by % per 1% increase in price at that price level. Thus, a large price ? increase decrease is advised.
(b) At what price will revenue be a maximum? (Round your answer to
two decimal places.)
yen
(c) Approximately how many paint-by-number sets will be sold per
month at the price in part (b)? (Round your answer to the nearest
integer.)
paint-by-number sets per month
In: Math
You just won $900 in the lottery and you decide to invest this money for 10 years. Three accounts pay as follows:
For each account, determine the value of your investment after 10 years.
If you are trying to earn the most money possible on your investment, which account should you invest your money in? (Select all that apply.)
In: Math
Consider the parametric curve given by the equations
x = tsin(t) and y = tcos(t) for 0 ≤ t ≤ 1
Find the slope of a tangent line to this curve when t = 1.
Find the arclength of this curve (make sure to do it by
integration by parts if you find yourself integrating powers of
sec(θ))
In: Math
Find the mass and center of mass of the solid E with the given density function ρ.
E is the tetrahedron bounded by the planes
x = 0,
y = 0,
z = 0,
x + y + z = 3;
ρ(x, y, z) = 7y
In: Math
Find a polynomial p(x) with zeroes at 1,-2, and -1 and such that p(2) equals 6 ?
What is the remainder when the polynomial p(x) equals (x^101 - x^50 - 3x^9 + 2) is divided by (x+1) ?
Find a polynomial of degree 4 with zeroes at -2, 9, and 5. (NOTE: leave your polynomial factored; please do not expand it)
Factor the polynomial x^3 - 4x^2 + 3x + 2.
List all the possible rational roots of the polynomial 9x^7 + 2x^2 - 5x + 10. (NOTE: you are only asked to list them not to factor them)
Solve the equation 2x^3 - 3x^2 - 11x + 6 = 0 given that -2 is a zero of f(x)= 2x^3 - 3x^2 - 11x + 6.
For the rational function f(x)= 2x^2 - 1 divided by x^2 - 9, find the vertical asymptotes, if any. It's horizontal asymptotes, if any. It's X intercepts with multiplicity, if any. It's Y-intercept, if any.
Solve the inequality (X - 3) divided by (X - 2) less than or equal to 0.
Solve the inequality (X + 5)(1 - X) is greater than or equal to 0.
For the rational function f(x)= 4X divided by (x^2 - 4) find its Verticle Asymptotes, if any. It's Horizontal Asymptotes, if any and the end behavior. It's X-intercept, if any. It's Y-intercept, if any.
For the function f(x)= (x - 4)^2 - 1, find the vertex and the x and y intercepts. The equation of the axis of symmetry.
In: Math
1. Find the average value of the function f(x)= 1/ (x^2-9) on the interval from 0 ≤ x ≤ 1
2. Find the arc-length of the function f(x)= x^2 from 0 ≤ x ≤ 2
In: Math
Hyperbolas 4(y - 1)^2 - (x + 4)^2 - 36 =0
find the x- and y- intercepts. label on graph
state the domain and range
In: Math
Find the general solution of the equation:
y^(6)+y''' = t
In: Math