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Calculus Questions
Let r = < et, sin t, et >. Compute v, a, aT, and aN.
A moving particle starts at an initial position r(0) = <1, 0, 0> with initial velocity...
Determine D_t [r (t) x u (t)] given r(t) = cos9t) i + sen (t) j...
Find the general solution: y' = x - y
Find the local maximum and minimum values and saddle point(s) of the function. If you have...
Use the partial-fraction method to solve the following equation. dy/dx=(y+8)(y-7), where y(0)=5 The partial fraction constants...
Solve the following autonomous differential equation with the given initial condition. dx/dt=8-4x, where x(1)=-7 x=?
1. a) Find the solution to the system of linear equations using matrix row operations. Show...
Take the Curl of the following equations: ? (?, ?, ?) = 5??^2 (?) + ?^3?...
. A conical tank of with radius 5 m and height 10 m is filled with...
In Problems 17-20 use determinants to decide whether the system has (a) a unique solution or...
As the input value goes to infinity both exponential functions and factorials grow quickly. Which function...
7. Suppose that a golf ball is thrown vertically with an initial velocity of 40 meters...
Use the Lagrange Multipliers method to find the maximum and minimum values of f(x,y) = xy...
I want to build a rectangular fence against my house so I can foster three dogs...
A piece of wire 35 long is cut into two pieces . One piece is bent...
Suppose the Sunglasses Hut Company has a profit function given by P(q)=-0.01q2+4q-26, where q is the...
Find, correct to the nearest degree, the three angles of the triangle with the given vertices....
A telephone company wants to run a cable from a point A on one bank of...
The volume of a square-based rectangular box is 252 dm^3. The construction cost of the bottom...
A piece of paper for a poster has an area of 1m^2. The margins at the...
An environmental landscaping company wishes to run a pipeline from a pumping platform (R) located 15...
Find the volume of the solid under the surface z = xy and above the triangle...
Find the equation of the sphere with center in the xz- plane and passing through the...
if g(x,y)= (x^2)+(3y^2)-2x a) what is the only critical point b) at the critical point, does...
A real estate office handles a 80-unit apartment complex. When the rent is $550 per month,...
Heller Manufacturing has two production facilities that manufacture baseball gloves. Production costs at the two facilities...
A hemispherical bowl with a radius of 6 feet is full of water. If the density...
Question #3: (4 pts per part) Show all steps to receive credit. (a) Suppose a particle...
find the radius of convergence, R, of the series. Sigma n=1 to infinity x^n/(4^nn^5) R= Find...
use the definition to find L[e^2t(cos2t)] Laplace transform. If you use tables automatic thumbs down. Thank...
1.A conical tank has height 3 m and radius 2 m at the top. Water flows...
find absolute max and min f(x)= ln(x^3 -2x^2 +x) [1/4, 3/4]
For Partial Fractions, what is the purpose of Partial Fractions (i.e. how it is applicable in...
2. a) Consider the function y = sin x . State the following derivatives: i) y'...
Evaluate Integral (subscript c) z dx + y dy − x dz, where the curve C...
For a writing tangent line equations, what is the purpose of tangent line equations (i.e. how...
For a general limit problem, what is the purpose of limits (i.e. how it is applicable...
Using first principles of calculus, find the gradient of the tangent to the curve at ?...
If f is a differentiable function such that f′(x) = (x^2− 16)*g(x), where g(x)>0 for all...
Regarding y as the independent variable and x as the dependent variable, find the slope of...
A monopoly sells in two countries, and resales between the countries are impossible. The demand curves...
PART A: Find the Taylor series for ln x centered at x = 5 PART B:...
How do i find an indeterminate limit by hand? ex. limit as x approaches inf. (x^2)*e^(2x)...
2.) A golf ball launched vertically upward from the surface of Pluto with a velocity of...
9. (3 pts) Find the partial derivatives, as listed, of the function g(x,y) given below. gx(x,y)...
Use the following expressions for left and right sums left sum = f(t0)Δt + f(t1)Δt +...
Estimate the area under the graph of f(x) = 4 cos(x) from x = 0 to...
Find the area of the region lying to the right of x = y2 + 11y...
1)Consider the curve y = x + 1/x − 1 . (a) Find y' . (b)...
A surveyor is standing 30 feet from the base of a building, measures the angle of...
The price p (dollars per unit) of a particular commodity is increasing at the rate p...
The marginal cost is given by 2( 3q - 1)3 dollars per unit, where q is...
Authorities conducted an investigation and found that the chemical Trioxin was illegally dumped into the local...
curvature of (t, 3 cos(t), sin(t))
A constant force F=10i+3j−6k moves an object along a straight line from point (10, 3, 5)...
A study of a country's colleges and universities resulted in the demand equation q = 20,000...
Evaluate the line integral ∫CF⋅dr, where F(x,y,z)=5xi+yj−2zk and C is given by the vector function r(t)=〈sint,cost,t〉,...
(1 point) Find the volume of the solid obtained by rotating the region bounded by the...
I cannot see it, I need a different pair of eyes. The tangents of the equation...
. Find the length of the trajectory of the curve defined below. r(t) = 〈 t^2...
Problem 10. Let F = <y, z − x, 0> and let S be the surface...
Problem 7. Consider the line integral Z C y sin x dx − cos x dy....
f (x) = ex/x2 Find the Domain of f(x) Does the function have x- or y-...
Find the volume of the solid obtained by rotating the region bounded by the given curves...
Solve the following equation using integrating factor. y dx + (2x − ye^y) dy = 0
For each of the following vector fields F , decide whether it is conservative or not...
Find the work done by the force field F(x,y,z)=2xi+2yj+7kF(x,y,z)=2xi+2yj+7k on a particle that moves along the...
I'am working on a project where I need to calculate the best-fit; linear, quadratic, and exponential...
PLEASE WRITE CLEAR SO I UNDERSTANAD YOUR HANDWRITING THANK YOU Q1 Find the nth Maclaurin polynomial...
Minimizing Costs A pencil cup with a capacity of 45 in.^3 is to be constructed in...
Minimizing Construction Costs The management of the UNICO department store has decided to enclose a 915...
Maximizing Profits The quantity demanded each month of the Walter Serkin recording of Beethoven's Moonlight Sonata,...
Consider the function f(x,y) = ( x2 + z2)ln(y) a)Find the gradient of f. b) Find...
An artist has decided to finish their piece of artwork by balancing it on a fulcrum...
You want to build a 1100 square foot rectangular infinity pool. Three of the sides will...
Find the length of the trajectory of the curve defined below. r(t) = 〈 t 2...
For the function f(x) = ln(4x), find the 3rd order Taylor Polynomial centered at x =...
Let u and v be vectors in 3-space with angle θ between them, 0 ≤ θ...
3. A fire alarm has speakers at either end of a 10 m long corridor. The...
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