Find the radius and interval of convergence of the series X∞ n=1 3^n (x − 5)^n/(n + 1)2^n
In: Math
Use Lagrange multipliers to show that the shortest distance from the point (x0,y0,z0)
to the plane ax+by+cz=d
Is it the perpendicular distance? (Remind yourself of the equation of the line perpendicular to the plane.)
How to solve it
In: Math
Determine the location of the center of mass of the region
bounded above x^2 + y^2 = 100 and below y = 6. Assume the region
has a uniform
density.
Two answer I got were (0, -64/9) & (0, ((2048/3)/100arcsin(4/5)) -48))
In: Math
Evaluate the integral. (Use C for the constant of integration.)
√(-x^2-6x+27)
In: Math
1. Find the critical numbers for the following functions
(a) f(x) = 2x 3 − 6x
(b) f(x) = − cos(x) − 1 2 x, [0, 2π]
2. Use the first derivative test to determine any relative extrema for the given function
f(x) = 2x 3 − 24x + 7
In: Math
Consider the function
f(x) = x 4 − 4x 2 . Determine the following:
• The (x,y) coordinate pairs of the local minima and local maxima.
• The (x,y) coordinate pair of the absolute minimum and absolute maximum, should they exist. If the absolute min/max is obtained at multiple points, list all of them. • The intervals of increasing and decreasing.
• The intervals of concavity. That is, explain exactly where this function is convex and exactly where this function is concave.
• The (x,y) coordinate pair of the inflection points.
• The horizontal and vertical asymptotes, should they exist.
• The (x,y) coordinate pair of the roots.
In: Math
Find the maximum volume of a rectangular box that can be inscribed in the ellipsoid ?^2/81+?^2/36+?^2/36=1 with sides parallel to the coordinate axes. Volume =
In: Math
Find the maximum volume of a rectangular box that can be inscribed in the ellipsoid ?^2/81+?^2/36+?^2/36=1 with sides parallel to the coordinate axes. Volume =
In: Math
7. Find the maximum and minimum of the function. f (x, y) = x^ 2 + y^ 2 − xy − 3x − 3y on the triangle D ={(x, y)| x ≥ 0, y ≥ 0, x + y ≤ 4}
In: Math
| The length, width, and height of a box are measured as 5 ft, 4 ft, and 8 ft, respectively, with an error in measurement of at most 0.3 ft in each. Use differentials to estimate the maximum error (in feet) in the calculated volume of the box. |
In: Math
A rectangular storage container with an open top is to have a volume of 10 m3. The length of this base is twice the width. Material for the base costs $10 per square meter. Material for the sides costs $6 per square meter. Find the cost of materials for the cheapest such container. (Round your answer to the nearest cent.)
In: Math
Consider the equation f(x,y) = −4x2+4x+y2+2y, the picture shows some of it’s level curves.
a. Completing the square, write the equations and identify the traces f(x,y) = k for k = −1,0.
.(b) Draw the direction of fastest increase at the point (1, 1)
.(c) Find the rate of change of f (x, y) = z at (1, 1) in the direction of 〈−1, −2〉.
.(d) Find an equation for the tangent plane to the graph of f at (1, 1, 3).
In: Math
A positive number is added to the reciprocal of its square root. Use Calculus methods to answer the following questions:what if anything, is the smallest such sum? What, if any, positive x-values will yield the smallest sum? Give exact answers as well as answers accurate to Five decimal place. Be sure to give a mathematical justification that you answer represents a minimum and not a maximum.
In: Math
A machine that costs $5000 is to be replaced in 5 years by a new one. The old machine at that time would be worth $500. How much should the periodic payments be so that there will be enough money to buy a new machine (at the same price) if equal payments are made at the end of each semi-annual period at an annual interest rate of 6% compounded semi-annually? R= Answer Suppose an annual interest rate of 8% compounded semi-annually is used. What is the decreased semi-annual payment?
In: Math
Solve the initial value problem z(5)+ 2z'''- 8z' = 0, where z(0) = 4, z'(0) = 2, z"(0) = 8, z"'(0) = 12, and z(4)(0) = 8
In: Math