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solve using the laplace transform y''-2y'+y=e^-t , y(0)=0 , y'(0)=1
Solve by eliminating the arbitrary functions: U = f (y-2x) + g (2y-x)
Find the family of curves orthogonal to y^3 = kx
Find ?=∬? ???? bounded by ?=?^2 and ?−?+2=0
Find the absolute maximum and minimum values of f (x) = x^3 − 6x^2 + 9x...
Find the radius of convergence for ∞∑n=1(n!/n^n)x^n.
Differentiate the function y=ln(e-x +xe-x) Find y and y" y=ln(sec(3x)+tan(3x)) Use logarithmic differentiation to find the...
The partial fraction decomposition of 6x/8x2−10x+3 can be written in the form of f(x)/2x−1+ g(x)/4x−3,where f(x)=?...
Show all of your work neatly whenever possible. Justify your answers. 10. Find the absolute maximum...
Solve the linear programming problem by the simplex method. (There may be more than one correct...
Show all of your work neatly whenever possible. Justify your answers. For 5-8, consider . ....
Consider the following function. f (x, y) = (x − 6) ln(x5y) (a) Find the critical...
Consider the following function. H(x, y) = ln(5x^2 + 8y^2) (a) Find fxx(2,3) . (b) Find ...
4. Solve the homogeneous equation xdy = (y + 2)dx given y(3) = 10.
1.) Let f(x,y) =x^2+y^3+sin(x^2+y^3). Determine the line integral of f(x,y) with respect to arc length over...
Evaluate the surface integral. S x2yz dS, S is the part of the plane z =...
Consider the vector field F= <ey+ycosx , xey+sinx> . a) are the conditions for this field...
3. Consider the equation (3x^2y + y^2)dx + (x^3 + 2xy + 5)dy = 0. (a)...
What are the horizontal and vertical asymptotes of 1/(1+e^x). And compute the lim x infinity and...
A farmer wants to fence in a rectangular plot of land adjacent to the north wall...
Evaluate the integral ∫ csch4 ? coth7 ? ?x csch x = csc x , coth...
f(x,y) = x^2+y^2+4x-4y Find the extreme values of f on the circle x^2+y^2 = 9 by...
Chapter 8, Section 8.6, Question 014 The quantity, Q, of a certain product manufactured depends on...
About convex function: (1) Please show that f(x) = ax2 + bx + c is a...
Use Lagrange multipliers to find the maximum and minimum values of f(x,y)=xy subject to the constraint...
Consider the function ?(?, ?) = 10 ? ? ?^ (−0.3? 2−0.2? 2) A. This function...
Find the slope of the tangent line to the given polar curve at the point specified...
The Cartesian coordinates of a point are given. (a) (−4, 4) (i) Find polar coordinates (r,...
Let f(x,y) = sqrt(22−2x^2−y^2). Find the linearization of the function f at (1,2) and use it...
Solve the initial-value problem y''+5y'+6y=0, y(0)=1, y′(0)=−1, using Laplace transforms. When writing your answer limit yourself...
use Lagrange multipliers to find the maximum of F(x,y,z)=xyz with the constraint H(x,y,z)=x^2+y^2+z^2-8=0
A ladder 25 feet long is leaning against the wall of a house. The base of...
PROBLEM: Given f(x)=4x - x2 + k & (1,3+k) on the graph of f. (K=3) a)...
A right-circular cylinder with volume of V 3 m is to be constructed. Find the dimensions...
Find the absolute min and max values of the function f(x, y) =x + y− x^2y...
Use integration to derive the formula for the area of an ellipse with equation x^2/a^2+ Y^2/b2...
Find the linearization of the function f(x,y)=√(22−1x2−3y2 )at the point (-1, 2). L(x,y)=_______ Use the linear...
Find an equation of the tangent plane to the surface z=−3x2−1y2−2x+1y−1 at the point (4, 2,...
Find the general solution to the differential equation dy/dx=sinxcos2xtany. (Hint: If you have forgotten the integral...
(3) Let D denote the disk in the xy-plane bounded by the circle with equation y2...
Find the linear approximation of the function f(x, y, z) = x2 + y2 + z2...
Find the absolute extrema of the given function on the indicated closed and bounded set R....
In the Midpoint Rule for triple integrals we use a triple Riemann sum to approximate a...
1. Find the area between the curves. ? = ? 2 , ? = 2? −...
3. Find the equation of the tangent line to the curve 2x^3 + y^2 = xy...
Find a power series representation for the function: ?(?)=?^(2)arctan(?3) ?(?)=(?/(2−?))^3 Express the antiderivative as a power...
f(x)=ln ((x-2)/(x+2)) Find:intervals where concave down intervals of increase f(x)=(x^3)+ln(3x) Find:critical numbers
Find the volume of the region bounded by z=x^2+y^2-1 and z=1-x^2-y^2.
A 1-kilogram mass is attached to a spring whose constant is 16 N / m, and...
For the following functions, find the Maclaurin series: f(x)=e^xsinx.
12. Find the equation of the following planes: (b) pass through the point (1,-1,-1) and parallel...
Solve the following initial value problem, showing all work. Verify the solution you obtain. y''-2y'+y=0; y0=1,...
An antiderivative of (90t + 540)(t^2 + 12t)^(1/2) is A. 30(t^2 + 12t)^(3/2) B. (t^2 +...
It is given that ∑an (an >0) is convergent a) What can be said about the...
If f(x) = sin(x^6), find the value of (f^(42))*0.
Calculate derivatives for the following, Use proper notation. a) y=3x^5+4x+6 b) ?(?)=3√? + 5 ?3 c)...
Use the Chain Rule to find the indicated partial derivatives. N = p + q p...
Approximate the zero for f(x) = (x^3)+(4x^2)-3x-8 using newton's method Use x1 = -6 A)Find x2,x3,x4,x5,x6...
Find the area that lies simultaneously outside the polar curve r = cos θ and inside...
A farmer wants to fence a rectangular area of 50 square miles that borders a straight...
Classify the series as absolutely convergent, conditionally convergent, or divergent: ∞ ∑ ((−1)^?) (1)/√(?(?+1)) ?=1
evaluate the integral (x^3+4)/(x^2+4)dx show appropriate alegrabic work
Solve the Euler Equation t^2(y'')-5ty'+9y=0, t>0
Perform two iterations of the gradient search method on f(x,y)= x2+4xy+2y2+2x+2y. Use (0,0) as a starting...
Write the equations in cylindrical coordinates. 9x2 − 3x + 9y2 + z2 = 9 //...
Three numbers x, y, and z that sum to 99 and also have their squares sum...
Solve the following DE by the method of undetermined coefficients: y”-y’=10x-7e^x
Find the absolute extrema of the given function on the indicated closed and bounded set R....
Consider the following. f(h, k) = (32h3 + 15h2 − 10h + 47) · (43k +...
Show algebraically (ie don’t graph and give me a sketch for your solution) how the planes...
A police officer in a helicopter is hovering 1110 feet directly over a straight stretch of...
given the following functions, evaluate the derivatives dy/dt of the following functions. y=10t −6t+8 y =...
please show all work and circle answer if you cant do all the parts please don't...
Use the integral test to determine the divergence or convegence of the series (1/ (ln(5))^n) )...
Use Newton's method to estimate the two zeros of the function f(x)=x^4−x−12. Start with x0=−1 for...
Suppose that a population develops according to the following logistic population model. dp/dt=0.04p-0.0001p^2 What is the...
A rectangular box with a square base has a volume of 4 cubic feet. If x...
Write down a cylindrical coordinates integral that gives the volume of the solid bounded above by...
Let ?(?) = ?? ? + ?? ? . Find the following information and use it...
Find two + numbers x and y whose product xy is 8 and whose sum is...
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