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Calculus Questions
Derive the Cartesian coordinates of an inverted Cycloid
Find the absolute maximum and minimum vaues of f on the set D. f(x,y)=x^2 + y^2...
find the directional derivative of f(x,y) = x^2y^3 +2x^4y at the point (3,-1) in the direction...
A 5400 SUV is parked on a slope of 18 degrees. Use a projection to determine...
if f(x) = 1/(x^2+1) find the following: increasing and decreasing interval concave up and concave down
Let P(t) represent the number of people who have been infected by a disease t days...
x2 + (y-1)2 = 1 about the y-axis, find the volume
How to use laplace transform to solve the following problem ? y'' - 10y' +9y =...
Find an equation for the tangent plane to x^3+xy^2=3z at the point(2,2,16/3)
John sells necklaces on the beach. He sold the necklaces for $10 each and his sales...
A rectangular garden 800 m^2 is to be fenced off against monsters. One side of the...
For f(x)=2+3x+x3 find: A.increasing and decreasing intervals B. Local max and min coordinates C. Concativity Intervals...
Find the volume of the parallelepiped defined by the vectors ⎡⎣⎢−222⎤⎦⎥,⎡⎣⎢1−32⎤⎦⎥,⎡⎣⎢−50−1⎤⎦⎥.
A grain silo consists of a cylindrical concrete tower surmounted by a metal hemispherical dome. The...
Find the directional derivative of the function at the given point in the direction of the...
Use the Divergence Theorem ∬SF⋅dS=∭D∇⋅FdV ∬ S F ⋅ d S = ∭ D ∇ ⋅...
The rate of a continuous money flow starts at $800 and increases exponentially at 3% per...
During the first twenty years of business, this company's profit is given by: P(t) =...
Use the Divergence Theorem to evaluate S (11x + 2y + z2) dS where S...
Find the particular solution to y′′+9y=6sec(3t). Do not include the complementary solution yc=C1y1+C2y2. y=
My pension plan is an annuity with a guaranteed return of 5% per year. (Assume compounding...
A campground owner has 1900 m of fencing. He wants to enclose a rectangular field bordering...
Evaluate the line integral ∫F⋅d r∫CF⋅d r where F=〈sinx,−3cosy,5xz〉 and C is the path given by...
1. A solid is generated by revolving the region bounded by y=(9-x^2)^1/2 and y=0 about the...
Explain how we defined "e" in Calculus I in terms of exponentials and tangent lines and...
Show that the curve y = 7ex + 6x + 5x3 has no tangent line with...
given that f'(x)=-3x^2 -6x answer the following what inteeval is f(x) increasing or decreasinf find x...
The position of an object at time t is given by: r(t)=e^−t i + e^t j...
hello, my question is, how can i use implicit differentiation to calculate the optimal surface area...
44)A ball is tossed up from an 80 foot tower, with an initial velocity of 64...
What is the volume of the solid obtained by rotating the region bounded by the curves...
Find the equation of the tangent line to the curve r = 2 sin θ...
Calculate the area, in square units, of the region bounded by the line x=2 on the...
Determine which of the following equations are well defined functions with an independent variable x. Explain....
A pencil cup with a capacity of 48 in^3 is to be constructed in the shape...
Consider the functions f(x) and g(x), for which f(0)=2, g(0)=4, f′(0)=12 and g′(0)= -2 find h'(0)...
Set up an integral using the shell method to find the volume of the solid generated...
(1 point) Consider the function f(x)=x^2 e^6x f(x) has two inflection values at x = C...
Find the number of units x that produces a maximum revenue R. R = 180x2 −...
Find the area inside of r=1+cos theta, but outside of r=1+sin theta
1. Evaluate the integral: 1) ∫ ? 2? ???? ?? 2) ∫ ? 2 ?? ?...
If an open box has a square base and a volume of 111 in.3 and is...
For the function below, find a) the open intervals where the function is increasing b) the...
9) find the integral using trigonometric substituition integral of ((x^2)/ sqroot(9 - x^2)) dx
Find the length L of the curve R(t)=5cos(t)i−5sin(t)j+3tk over the interval [2,5]. L= ?
A closed box with a square base is to have a volume of 2000in2. The material...
find an equation of the tangent plane to the surface z=4x^5+8y^5+2xy at the point (-2,1,-124)
When the areas cross over the lower bounding curve ( including X axis if that is...
What is the parameter which decides whether a function is concave or convex towards the X...
1) Find the antiderivative if f′(x)=x^6−2x^−2+5 and f(1)=0 2)Find the position function if the velocity is...
Solve the differential equation(be sure to include detailed steps): y'-2y+4=0, y(1)=4
6. a) Use the given acceleration function and initial conditions to find the position at time...
Find the center of mass of one loop of the mathematical rose ? = cos(3?) (Not...
A local electronics store estimates that when x computers are sold in a month, the revenue...
Find the absolute extreme values of f(x) = (x2 + 2x)3 on the interval [−2,1].
y'' + 4y' + 4y = 12e^-2t y(0) = 3 y'(0) = -1 find particular soln.
The height, width and length of a closed rectangular box are changing by 1m/s,2m/s and 1m/s...
Suppose a product has a marginal revenue MR=150 and a marginal cost MC=x+40, with a fixed...
Find the equation of a line through the point (4, -3, 1) and is perpendicular to...
Compute the average value of the function f ( s ) = sin^3 s cos^8 s...
convert polar coordinates (3, 5pi) to cartesian coordinates.
(a) Find the distance between the skew lines l1 and l2 given with the vector equations...
Apply the row operation R1 + 2R3 → R1 on the following matrix: 2...
f(x)=x^3+1 and g(x) =x^-2 find rule for function f-g
1. Find f''(x) F(x)= (x^2+2)^9 F''(x)= 2. Find t^(4)(n) for the function t(n)= 2n^-1/2+7n^3/2 t^(4)(n) =...
1) What is the parameter which decides whether a function is concave or convex towards the...
For each of the following, i) write a general formula that has level curves of the...
Compute ∬S (x)(y^2)(z) dS where S is the part of the cone with parameterization r(u,v)= <ucosv,usinv,u>...
: Consider f(x) = 3 sin(x2) − x. 1. Use Newton’s Method and initial value x0...
Using Lagrange multipliers, find the global maxima and minima of the function f( x , y...
Set up BUT DO NOT SOLVE an integral or integrals that give the area between the...
use f(x)=2x^4-4x^2-4 to answer the following. a) find where f(x) is increasing or decreasing b) find...
(i) Use the Intermediate Value Theorem to prove that there is a number c such that...
An open box is to be made from 72 square meters of cardboard, and the length...
y'''+2y''-4y'+8y= -5cos(x)-10sin(x)+16e2x A.Solve the underlining homogenous equation, solve the characteristic equations, write fundamental solutions B. Find...
Find the distance travelled by the particle during the first 4 seconds when a particle moves...
a. Is F(x,y,z)= <(e^z)siny,(e^z)cosx,(e^x)siny> a conservative vector field? Justify. b. Is F incompressible? Explain. Is it...
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