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Identify the surfaces with the given vector equations r(u,v) = <2usin(2v), 3u^2, 2ucos(2v)> r(u,v) = <2u,...
Find f. f "'(x)= cos(x), f(0)=3, f'(0)=5, f "(0)=5
please answer A water tank has the shape obtained by rotating the curve y = x...
A corporation creates a sinking fund in order to have $760,000 to replace some machinery in...
1) Show that the formulas below represent the equation of a circle. x = h +...
The region is bounded by y=2−x^2 and y=x. (a) Sketch the region. (b) Find the area...
Find the derivative of the given expression. f(x)=17x^2+ln(x^3) f'(x)= Solve the following equation for x: ln(x−4)+ln(x−2)=ln(8)ln(x−4)+ln(x−2)=ln(8)...
Find the area of the region enclosed between y=4sin(x) and y=4cos(x) from x=0 to x=0.4π. Hint:...
maximize B=xy^2,where x and y are positive numbers such that x+y^2=11
B has 360 cm of wire. She wants to build the wire frame of a rectangular...
Find ?y as a function of ?t if ?″+10?′+50?=0,?(0)=9,?′(0)=5.y″+10y′+50y=0,y(0)=9,y′(0)=5. ?=y= Note: This problem cannot interpret complex...
slove in any valid method: x^2y''-8xy'+20y=3x^2, im trying to solve via variation of parameters but im...
A computer dealer can sell 12 personal computers per week at a price of $2000...
(A.) Find the average value of the function f over the interval [5, 7]. f(x) =...
Find the absolute maximum and the absolute minimum values of f(x) = 4 x^3-13 x^2+10 x+6...
Consider the following. u = −6, −4, −7 , v = 3, 5, 2 (a) Find the...
Find the absolute maximum and minimum of f(x,y)= 3x+4y within the domain x^2+y^2 less than or...
A stone is thrown straight up from the edge of a roof, 950 feet above the...
Find the first two nonzero terms of the Maclaurin expansion of the given function: f(x)=cosx^2
A grain silo has the shape of a right circular cylinder surmounted by a hemisphere. If...
5. Let f(x) = xe^X. Solve f'(x) > 0. A) x >-2 B) x > 0...
1. Consider the geometric series −1/4+3/16−9/64+27/256+... Use summation notation to write this series and determine whether...
Find the critical point of the function g(x)=ln(x^(2)+2x+3). Then determine whether the critical point is a...
Let Q1, Q2, Q3 be constants so that (Q1, Q2) is the critical point of the...
My Notes Ask Your Teacher Find the Cartesian coordinates of the given polar coordinates. Then plot...
A large shipping crate is to be constructed in a form of a rectangular box with...
Find the power series representation for the function: f(x) = x2 / (1+2x)2 Determine the radius...
A box with a square base and open top must have a volume of 202612 cm3....
Consider the boundary value problem y''(t) + y(t) = f(t) , y(0) = 0 and y(π/2) =...
Suppose f(x)=x6+3x+1f(x)=x6+3x+1. In this problem, we will show that ff has exactly one root (or zero)...
Find the moments about x and y, and the center of mass for the 2-d system...
Determine whether the sequence converges or diverges. If it converges, find the limit. (If an answer...
Verify that the equation y = x2+ 2x+2+Cex is a solution to the differential equation y'-y+x2=0.
1.Find the area of the region specified in polar coordinates. One leaf of the rose curve...
A piece of wire of length 55 is cut, and the resulting two pieces are formed...
Find the average of the function ?(?) = sin(?) + cos(2?) over the interval 0 ≤...
1. Write the equation for the following conic sections in standard form: (a) An ellipse centered...
You need to build a rectangular enclosure divided into 3 equal rectangular sections, occupying a total...
A car is traveling at 88 ft/s when the brakes are fully applied, producing a constant...
Find the general solution to the given differential equation. Then, use the initial condition to find...
When z=f(x,y)=2x+6y+1 is constrained by x²+y²=40, what become the minimum and maximum values?
Find the volume under the surface z=xy above the triangle with vertices (3,3,0), (8,3,0), (3,6,0).
A liquid is poured into a conical container with a base radius of 6 inches and...
Suppose that M is the absolute maximum and m is the absolute minimum of the function...
Which of the following sequences meet the conditions of the integral test? An = n(sin(n) +1)...
how do you take integral of 1/((x+1)(x+2)^2)?
Suppose that M is the absolute maximum and m is the absolute minimum of the function...
With the parametric equation x=cos(t)+tsin(t), y=sin(t)-tcos(t) , 0 ≤ t ≤ 2π) Find the length of...
For the following exercises, determine a definite integral that represents the area. Region enclosed by the...
(b)an auditorium has 45 seats in the 1st row, 52 seats in the 2nd row, 59...
Let the vectors a and b be: a = <0,-3,4> and b=<1,2,-2>. Find the following: a)...
A 100 L tank is initially filled to the brim with distilled water. An inflow valve...
You've decided to sell sweatshirts for the upcoming game. You project that at a price of...
Find the point on the line 4x + y = 7 that is closest to the...
Find the Taylor series and associated radius of convergence for ?(?) = cos? at ? =...
Find parametric equations of the line through the point (2, 1, 0), perpendicular to the plane...
Find the equation(s) of the tangent line(s) when x = 0 for: xy^5 +2(x^2)y−y^2 −3y−2=0
find the distance between the point (-1,3,5) and the line given by x=5+t, y=3-2t, and z=1-t
find an equation of the plane with the given characteristic. the plane passes through (-2,-3,4),(-2,3,1) and...
a straight piece of wire 10 feet long is bent into the of an L. What...
Rederive Cauchy’s integral formula from the Residue Theorem
Let f be a continuous odd function on straight real numbers. If integral subscript negative 5...
Find a definite integral that is equal to the area of the region bounded by ?(?)=?2+10?????(?)=6?+12....
The indicated function y1(x) is a solution of the given differential equation. Use reduction of order...
Use a Taylor series to get the derivative of f(x) = sin(x^2) and check for the...
find the orthogonal trajectories of the family of curves y=e^(kx)
Use a Taylor series to solve y'(t)-6y=9, y(0)=2
Consider the vector field →F=〈3x+7y,7x+5y〉F→=〈3x+7y,7x+5y〉 Is this vector field Conservative? yes or no If so: Find...
1. A rectangular pen is built with one side against a barn. If 600 m of...
Find an equation of the curve whose tangent line has a slope of f′(x)=4x−8/9 given that...
use the mean value theorem to show that: squareroot(y)-squareroot(x)<((y-x)/(2squareroot(x)) if 0<x<y
find the velocity of the particle after 8 seconds, given its acceleration a(t) = 12+sint at...
Series Solutions of Ordinary Differential Equations For the following problems solve the given differential equation by...
The future value of an investment of P dollars compounded n times per year with an...
Evaluate the surface integral S F · dS for the given vector field F and the...
The set of all X∈R2 × 2 that satisfies AX−XA = [000 0], where A is...
Consider the following. f(x) = 4x3 − 6x2 − 24x + 4 (a) Find the intervals...
The management of the UNICO department store has decided to enclose an 833 ft2 area outside...
Use the optimization process to find the point (?, ?) on the curve ? = √?...
A particle moves along a line with velocity v(t)= t-ln(t^2+1). What is the maximum velocity on...
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