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A company must build a cardboard box (without a lid) from a recycled cardboard sheet of...
A new McDonalds has an initial population of 99, which doubles in three and a half...
A piece of cardboard measuring 11 inches by 10 inches is formed into an open-top box...
Find the absolute maximum and absolute minimum values of f on the given interval. f(t) =...
Given that 1/ 1 − x = ∑ n = 0 x^n with convergence in (−1,...
Find d^2y/dx^2 . x = t^3 − 7, y = t − t^2 d^2y/dx^2=?
Find the volume generated by rotating the region bounded by y=sin(x), y=0, x=2π, x=3π about the...
Locate the relative extremum and point of inflection. Use a graphing utility to confirm your results....
Evaluate the integral ∫ cosht/sinh^2t(1+sinh^2t) by using the following two different methods: (a) make a substitution...
If z = x2 − xy + 4y2 and (x, y) changes from (1, −1) to...
Find the equation from the line to the curve r = 2 + sin3θ in t...
Sketch the region bounded above by the curve 2e^−x sin(πx), the x-axis, and x = 1,...
Glorious Gadgets is a retailer of astronomy equipment. They purchase equipment from a supplier and then...
What two real numbers x and y whose product is 25 will minimize x^3 + y^3...
Given the given cost function C(x)=5350+700x+1.5x2C(x)=5350+700x+1.5x2 and the demand function p(x)=2100p(x)=2100. Find the production level that...
Find the present value P of a continuous income flow of c(t) dollars per year using...
Use the Maclaurin series for cos(?) , ????(?), and ?? to evaluate the following limits: a....
1. Find the first six terms of the recursively defined sequence Sn=3S(n−1)+2 for n>1, and S1=1...
Solve the differential equation by using integrating factors. xy' = 4y − 6x^2 y(x)=?
The per capita growth rate of many species varies temporally for a variety of reasons, including...
Determine the point on the curve y=2-ex+4x at which the tangent line is parallel to the...
An open box is made out of a 10-inch by 18-inch piece of cardboard by cutting...
1) Verify that the function satisfies the three hypotheses of Rolle's Theorem on the given interval....
The function R(x) models the daily revenue generated by selling x calculators. What is the input...
Find the slope and the equations of the tangent lines to the given curves at each...
Verify that the function satisfies the three hypotheses of Rolle's Theorem on the given interval. Then...
Each time your heart beats, your blood pressure first increases and then decreases as the heart...
What are the absolute maximum and minimum values of the function f(x, y) = (x+ 3)^2+...
solved
let f(x) = sqrt x^4+4x+4.find the equation of the tangent line to the graph of f...
Consider the differential equation y”+5y’+6y=f(t). Write the form of the particular solution if f(t) is the...
(part a) Find the curl of F F(x,y,z) = (x cos(y))i + xy2j (part b) Find...
Find dw/dt using the appropriate chain rule for w=x^2+y^2+z^2 where x=8tsin(s), y=8tcos(s) and z=5st^2
Determine whether the Mean Value Theorem applies to f(x) = cos(3x) on [− π 2 ,...
Verify that the following function satisfies the hypotheses of the Mean Value Theorem on the given...
(a) Find parametric equations that describe the circular path of the tip of a 15-inch second...
Tangent Line Quiz Find the slope and the equations of the tangent lines to the given...
The demand for a product is D(x)=75-0.3x where x is the price in dollars. At a...
1) Determine if the sequence converges or Diverges. If it converges find the limit. an=n2*(e-n)
A carpenter wants to construct a closed-topped box whose base length is 2 times the base...
Let f (x, y) = xe xy. Find the maximum rate of change of f at...
Total revenue is in dollars and x is the number of units. Suppose that in a...
find the point on the graph of the given function at which the slope of the...
Find the dimensions of a rectangle whose area is 3600 meters squared and whose perimeter is...
The marginal price for a weekly demand of x bottles of shampoo in a drugstore is...
Evaluate the surface integral S F · dS for the given vector field F and the...
Use integration by parts to evaluate the integral: ∫ e^8r sin ( − 3r )dr
A particle that moves along a straight line has velocity v ( t ) = t^2e^−...
Suppose a Cobb-Douglas Production function is given by the following: P(L,K)=10L0.9K0.1 where L is units of...
Approximate the area under the graph of f(x) and above the x-axis with rectangles, using the...
Find the point on the surface ? = √ ? 2 + 2? 2 that is...
f(x) = 1/(x-2) + x - 2 a) Find the vertical and horizontal asymptotes. b) Find...
Consider the function f(x, y) = sin(2x − 2y) (a) Solve and find the gradient of...
Determine where the given function is increasing and where it is decreasing. f(x)=x4-2x2-9 f(x)=x2(6-x)2
1.Solve the following initial value problem a) dy/dx= y2/(x-3), with y(4)=2 b) (sqrt(x)) dy/dx = ey+sqrt(x),...
Take derivative implicitly (tan(4u) + z^2)^5 What's the derivative of 4sin^3(x^7) Sketch a rough graph of...
Find the dimensions of a rectangle with perimeter 96 m whose area is as large as...
Given the function g(x)=4x^3−24x^2+36x, find the first derivative, g'(x) g′(x)= ??? Notice that g'(x)=0 when x=1,...
Find the absolute max and absolute min of f(x)= x3 -x -1 on the interval [-1,...
A company produces two models of products, SUPER and ULTRA. Each SUPER model generates a profit...
The total weight of a cable hanging from the ceiling plus the bucket it is attached...
The equation of motioj of a partucle is given by s(t)= t^3 -6t^2 +9t where s...
∫ ?(? − 1)5??
If r = 1 + sin(3θ) is the equation of a polar graph, find the slope...
1- Solve Ordinary Differential Equations A) (xˆ2 + 1) y '+ 4xy = x B) y...
Suppose the wholesale price of a certain brand of medium-sized eggs p (in dollars/carton) is related...
A function f(x) and interval [a,b] are given. Check if the Mean Value Theorem can be...
What is the effect on the dot product of two vectors, if the angle between the...
Given f(x)=(x^2+x)cos(x) What is the taylor series for 'f' when a=0?
You have been asked to design a closed rectangular box that holds a volume of 25...
Eliminate the parameter to find a Cartesian equation of the curves: a) x=3t+2,y=2t−3 b) x=21sin(t)−3,y=2cos(t)+5
A projectile is fired with an initial speed of 180 m/s and angle of elevation 60°....
6. The volume of a cube is increasing at a rate of 10 cubic cm/min. How...
Show that increasing functions and decreasing functions are one-to-one. That is, show that for any x1...
Givenf(x)=x3−6x2+15 (a) Find the critical numbers of f. (b) Find the open intervals on which the...
1.) A rock is thrown into a still pond. The circular ripples move outward from the...
Graph the rational function. Provide the intercepts, asymtotes, critical numbers, open interval where function f(x) is...
Find f'(x) for the following. f(x) = (√x+1)(2x-3) Could someone explain this the quare root keeps...
Evaluate the triple integral _ D sqrt(x^2+y^2+z^2) dV, where D is the solid region given by...
Find the arc length of the curve on the given interval. (Round your answer to three...
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