Determine whether the given vectors are orthogonal, parallel or neither. <-5,3,7> and <6,-1,2> <4,6> and <-3,2> -i + 2j + 5k and 3i + 4j - k 2i + 6j - 4k and -3i -9j +6k Find a unit vector that is orthogonal to both i+j and i+k. If a = <3,0,-1>, find a vector b such that comp_a b = 2 (component of b in the a direction
Consider the equation: y'' + k*y = 0 with BC: y(0) = 0 , y() = a 0 Answer the following: 1. What are the restrictions on k such that there is a nontrivial solution? 2. Find a solution using eigenfunction expansion on [0,] 3. Find a solution to the differential equation using any method 4. Co
1. y'' + k*y = 0 BC: y'(0) = 0 y'(L) = 0 2. y'' + k*y = 0 BC: y(0) = y() y'(0) = y'() 3. y'' + k*y = 0 BC: y(0) = 0 y() +2*y'() = 0 4. y'' + 2*y' + (1+k)*y = 0 BC: y(0) = y(1) =0 Please see the attached file for
Let f(x)=(the integral from 0 to x^2) sint dt. At how many points in the closed interval [0, square root of pi] does the instantaneous rate of change of f equal the average rate of change of f on that interval. keywords: integration, integrates, integrals, integrating, double, triple, multiple
Please explain how/why: lim x---> - 1 x^2 - 1 / x+1 How would this change if the 1 was positive?
1) a = (1, 2, -2); ||b|| = 6. What choice of b will make the dot product a . b the least possible? 2) The plane P pass through the point M (2, 3, 1) and is parallel to vectors u = (1, -1, 4) and v = (2, 1, 0). Find the distance from the point N (3, 2, 4) to the plane P. 3) Find an equation of the plane that passes through (1,
1) Find the equation of the line passing through the point (6, 1, 8) in the direction of the vector (-3, 4, -2). Write the equation in vector and coordinate form. 2) Find the equation of the line segment joining points (2, 4, 6) and (1, 7, 8), both in vector and coordinate form. Be sure to specify the set of possible values o
4. What are the projections of the point (2, 3, 5) on the xy, yz-, and xz-planes? Draw a rectangular box with the origin and (2, 3, 5) as opposite vertices and with its face parallel to the coordinate planes. Label all vertices of the box. Find the length of the diagonal of the box. 8. Find the lengths of the sides of the tr
Determine the infinite limit #1)lim x-1/x^2(x+2) x->0, #2)lim csc x x->pi -, #3)lim ln(x-5) x->5+, #4)lim 6/x-5 x->5- #4) The slope of the tangent line to the graph of the exponential function y= 2^x at the point (0,1) is limx->0(2^x - 1)/x. Estimate the slope to three decimal places. keywords : find, findi
An open box of maximum volume is to be made from a square piece of material 24 inches on a side, by cutting equal squares from the corners and turning up the sides. See attached file for full problem description.
Find limit lim x---> - 4 x^2 - 16 / x+4 Please explain keywords : find, finding, calculating, calculate, determine, determining, verify, verifying, evaluate, evaluating, calculate, calculating, prove, proving
3. Today you visited the R & D (Research and Development) department of a pharmaceutical manufacturer. The people in this lab have to calculate the recommended dosage of the products they are developing. Medicine is expressed as a function of the concentration in parts per million, with the potency of the dosage declining over a
4. A retailer you spoke with in New York City's fashion district imports haute couture from European designers. One of the accommodations which must be considered when importing fashion from other countries is the difference in the size charts. A function that will convert dress sizes in the United States to those in Italy is
If y = XsinX prove that Y (X^2 + 2) - 2X dy/dx + X^2 d2y/dx2 = 0
(a) The function 1/t is continuous on the given interval, therefore integrable. The primitive is log(t). The primitive of exp(t) is exp(t). Therefore the integrals are: (b) The primitive of -cos(x) is -sin(x) anf the primitive of x is x2/2, therefore the integral equals: (c) We apply the so called Simpson's approximation:
Find the general solution to the following (d^4y/dx^4) + 4(d^3y/dx^3) + 8(d^2y/dx^2) + 8(dy/dx) + 4y=0
Find the general solution of the following (d^6y/dx^6) -3*(d^4y/dx^4) +3*(d^2y/dx^2) -y=0
Let s (n)= (sigma sign with n as upper bound and i=1 as lower bound) (1+(i/n))^2 * (1/n). Find the limit of s (n) as n approaches positive infinity.
Use the fundamental theorem of calculus to evaluate: (integral from 0 to 2) abs(x-1)*dx
Question: Evaluate the limit of e^(-x)*ln[x] as x approaches positive infinity. Please show all work.
Use power series to solve the second-order homogeneous equation : u''(t) - tu'(t) - 2u(t) = 0
Find the direction in which f(x,y,z) = ze^(xy) increases most rapidly at the point (0,1,2) What is the maximum rate of increase?
A particle of mass m moves under the influence of constant force f and the friction force γ(xdot)n Its equation of motion reads: m(x-double dot) + γ(xdot)n = f Find x(t) for n=1 and n=2 if x=0 and x-dot=0 at t=0 Check that your solutions exhibit the correct behavior in the limit. Please see the attac
Solve the differential equation: 1. f"(x) = x^2, f(0) = 0, f'(0) = 1 2. Find the area bounded by the graph of f(x) = x*sqrt(1 - x^2), the x-axis and the vertical lines x = 0 and x = 1. 3. Given the function f(x) = x^3 defined for 0 < x < 1 evaluate the lower and upper Riemann sums. 4. Use the fundamental theorem of
4. Find the center, vertices and foci of 4x^2 + 9y^2 -8x +36y +4 =0. Graph, labeling all relevant points including the foci. 5. Find the equation of the hyperbola whose center is the origin, vertex at (2,0) and focus at (3,0). Write the equation of the asymptotes. 6. Find the center, vertices, foci and asymptotes of
F(x,y)=1/(x^2+y^2) Is the domain (-infinity, 0) union (0, infinity)? Is the range (0, 1]? What are the x and y intercepts and is the z intercept undefined?
How do you find the x, y, and z-intercepts of a 3-Dimensional graph step by step? I am trying to interpret some graphs and would like this information to assist me in the interpretation. keywords: 3D, 3Dimensional
Find the volume of the solid that is generated by rotating the region formed by the graphs of y = 2x^2 and y =4x about the line x = 3 .
Please see attached file. 13. A series circuit consists of a resistor with R = 20 ohm, an inductor with L = 1 H, a capacitor with C = 0.002 F, and a 12-V battery. If the initial charge and current are both 0, find the charge and current at time t. 14. A series circuit contains a resistor with R = 24 ohm an inductor with L = 2
Solve differential equation using power / Taylor series. Need problems 2,4,6,8,10. See attached file for full problem description. 2. y' = xy 4. (x- 3)y' + 2y = 0 6. y'' = y 8. y'' = xy 10. y'' + x^2y = 0, y(0) = 1, y'(0) = 0.