Consider the function : f(x,y) = x(x-1)(x-2) + (y-1)(x-y) [QUESTION 1]find the maximum and the minim values of the directional derivative (df/ds)]u at ( 1 , 3/2 ) as u varies . ( (df/fs)]u : I can't write the symbol clearly but it means : the derivative of f according to s on the directi
Consider a triangle in the plane, with angles , a, b , c. Assume that the radius of its circle is equal to 1. 1) by decomposing the triangle into six right triangles having the incenter as a common vertex, express the area A of the triangle in term of a, b , c ( the answer should be a symmetric expression). Then use the resu
A population obeys the logistic model. It satisfies the equation dP/dt = 2/1300 P(13-P) for P>0 Assume P(0)= 3 Find P(74)
Find an explicit or implicit solutions to the differential equation: (x^2 + 4xy)dx + xdy = 0 "F(x,y) such that the solutions are F(x,y)=c for an arbitrary constant c".
The following differential equation is exact. Find a function F(x,y) whose level curves are solutions to the differential equation: ydy-xdx=0 "F(x,y) such that the solutions are F(x,y)=c for an arbitrary constant c".
The steady state deflection is given by: y''''+c^4*y=f(x) calculate and plot the deflection for a load: f = 1 for |x|<10, f=0 everywhere else. using Fourier transform. Plot the deflection for various values of c.
Limit f(x) (x to 1) and limit f(x) (x to -1), where f(x) = 1/x-1 if x < -1 x^2 + 2x if x is greater than or equal to -1
A closed box with a square base is to have a volume of 1,500 cubic inches. Express its surface area as a function of the length of its base.
Write an equation for the line with the given properties Through (2.5) and parallel to the y axis.
Find the slope and intercepts of the given line and draw a graph. X+3/-5 + y-1/2 = 1
H(u)= ^4 to the square root of u^2-4
Please see the attached file for full problem description.
Please see the attached file for full problem description. --- Let S denote the closed cylinder with bottom given by z=0, top given by z=4, and lateral surface given by the equation x^2 + y^2 = 9. Orient S with outward normals. Determine the indicated scalar and vector surface integrals.
Find dy/dt of the function y= 2/(2t^3-5)^4 Could you please explain each step required to complete this question?
Evaluate the iterated integral (See attached) SEND ANSWER AS ATTACHMENT
Here is the problem: Find the volume under the plane z = 4x + 2y + 25 and over the region bounded by y = x^2 - 10 and y = 31 - (x-1)^2
Tangent and Normal (III) (Differential Calculus) Find ds/dr for the curves: (a) r = a? (b) r = a/? See attached file for full problem description.
Tangent and Normal (II) (Differential Calculus) Find ds/d? for the curves : (a) r2 = a2cos2? (b) rn = ancosn? See attached file for full problem description.
Find the General Solution of the equations. (a) r = a2t (b) r - 3as + 2a2t = 0 where r = ∂2z/∂x2 , s = ∂2z/∂x∂y, t = ∂2z/∂y2 (c) (2D2 + 5DD′ + 2D′2)z = 0 (d) ∂3z/∂x3 - 3∂3z/∂x2∂y + 2∂3z/∂x∂y2 = 0
I am having difficulties gaining a solution for the following differential equation of x'=2t3 -6t2 + t1/2. Could I please get assistance with detailing my solution.
Use the method of Lagrange multipliers to find the indicated extremum. You may assume the extremum exists. Find the maximum and minimum values of f(x,y,z) = x + 3y - z subject to z = 2x^2 + y^2
Find the critical points of the given function and classify each as relative minimum, relative maximum, or a saddle point. f(x,y) = x^2 + 2y^2 - xy + 14y
Please see attached file for various questions in Calculus. Thank you for your help.
Laplace Transformation Question. Please see attachment.
Laplace Transformations See attached for questions
Show that equation is of exponential order and not of exponential Order. (please see attachment for details)
Solve (see in attachment) without using partial fraction decompositions. Thanks you
Solve y(t) + int [(t-tau)*y(tau), tau=0..t) = exp(t).
What are the domain and range and x intercepts of the function? Approximate to two decimal places. y=-x^2-20x-3
The total profit in dollars for the sale of n microwave ovens is given by p=-2n^2+140n-174 what value of n will provide the maximum profit. Please show all work including the line graph.