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Calculus Questions
A forest fire covers 100 acres at a time t=0 (hours). The area of the fire...
find the volume of the solid below the surface z=2-square root ( 1+x2+y2)and above the xy-plane...
A) Show that the equation represents a sphere, find its center and radius: x2+y2+z2-2x-4y+8z=15 B) Find...
Find a and b such that y=asinx+bcosx satisfies the differential equation y''+y=6sinx+cosx
Consider the following parametric equation. x=4(cosθ + θsinθ) y=4(sinθ − θcosθ) What is the length of...
At a certain factory, the marginal cost is 3(q - 4)2 dollars when the level of...
Find the area of the region enclosed by the astroid x=9cos3(θ), y=9sin3(θ).
Find the relative extrema, if any, of the function. Use the Second Derivative Test if applicable....
The pressure, volume, and temperature of a mole of an ideal gas are related by the...
Use Laplace transformation to find the convolution product: t^2 * (420t^4 + 60t)
Suppose f(x,y,z)=x2+y2+z2f(x,y,z)=x2+y2+z2 and WW is the solid cylinder with height 55 and base radius 44 that...
A) Find the angle between the vectors 8i-j + 4k and 4j + 2k B) Find...
Let E be the solid that lies in the first octant, inside the sphere x2 +...
Evaluate the triple integral ∭ExydV∭ExydV where EE is the solid tetrahedon with vertices (0,0,0),(10,0,0),(0,1,0),(0,0,10)(0,0,0),(10,0,0),(0,1,0),(0,0,10).
Find the absolute maximum and minimum values of the following function on the given interval. If...
Can you think of a cost function, so that the marginal cost at any x is...
An annuity has interest of 9% per annum compounded monthly. If payments of $200 are made...
Use Newton's method to approximate an intersection point between ?(?)=tan(?) and ?(?)=2?. Use the initial value...
Use a double integral to find the area inside the circle r = cos θ and...
Classify and solve the differential equation y''-y' = 5e^x - sin2x
You are standing in a very long line, waiting to enter an arena to attend a...
1. Sketch the direction field for the following differential equation dy dx = y − x....
Consider the function ?(?,?)=3?^3−4??−5?^2. Find the maximum and minimum values of ? f in the region...
Compute the following limits and show all your work: (a) 5pts A = limx→∞· 4x^2 −3/x^2...
A projectile is launched at a height of 5ft. On the ground with an initial speed...
Apply the Laplace operator to the function ℎ(?,?,?)=?^(3?)sin(−9?).
A resort can rent 100 canoes a day when they charge $30 per canoe for a...
Verify Stokes’ theorem.
Use Lagrange multipliers to find the maximum and minimum values of f(x,y)=4x3+y2 subject to the constraint...
Compute the following limits using l'H\^opital's rule if appropriate. Use INF to denote ∞ and MINF...
Consider the region bounded by y=sqrt(x) and y=x^3 a) Find the area of this region b)...
Use the definition of the derivative to show that f(x) = |x^2 – 9| is not...
If y= 1/(1+tanx)^2 ,find y' y''
Find the local maximum and minimum values and saddle point(s) of the function. If you have...
A small lake, which is initially clean and has an initial volume of 40,000 cubic meters,...
Suppose you are climbing a hill whose shape is given by the equation z = 900...
Find the area under the curve ? = ? − ???(?), ? = 4(1 − ???(?))...
Use the method of Lagrange multipliers to find the extreme values of f(x,y)= x^(2) + y^(2)...
The function f(x) = loga(x2) has a tangent line when x = 1 that passes through...
If f(x) = 2x2 − 7, 0 ≤ x ≤ 3, find the Riemann sum with...
let S be the surface defined by x^4-2x^2y^2+3z^2=12, Find the equation of the tangent plane to...
The CEO of the soda company Pepsi calls and tells you that the company needs to...
Let f(x) = x2, and compute the Riemann sum of f over the interval [5, 7],...
Find the center of mass of the triangle with vertices (-2,-2), (4,-2), and (4,4). SOLVE THIS...
To find the relative extrema, use the second derivative test if applicable. g(s)=s/(1+s2) Please show steps
solve the Cauchy-Euler Initial value 9t2y''' + 15ty'+y= 0 with y(1) = 6 and y'(1) =1
A piece of wire of length 5353 is cut, and the resulting two pieces are formed...
The length, width, and height of a box are measured as 5 ft, 3 ft, and...
Calculate the work (in joules) required to pump all of the water out of a full...
An heiress receives an income stream from a will at a rate of f(t) = 40,000e0.023t...
Please explain in detail of why addition and multiplication complex numbers are defined the way they...
Test the series for convergence using the Alternating Series Test: X∞ m=2 (−1)^m/ (m 2^m). If...
A company's total sales (in millions of $) t months from now is given by the...
Find the particular antiderivative that satisfies the following conditions: A) p'(x)=-20/X^2 ; p(4)=3 B) p'(x)=2x^2-7x ;...
Find the local maximum and minimum of the function f(x) = x+10*sqrt(3-x)
Question 11: What is the general solution of the following homogeneous second-order differential equation? d^2y/dx^2 +...
The weekly cost (in dollars) of producing x compact discs is given by C(x) = 2000...
Halle los primeros cinco (5) términos de la secuencia definida por an = (-1)n sin(1/n)
1. a) Use the Chain Rule to calculate the partial derivatives. Express the answer in terms...
Given f(x) = x4 – 4x3, graph the nonlinear function and answer the following: a) What...
Starting from the same intersection at different times, Alice walks due North at 3 miles per...
The top of a ladder slides down a vertical wall at a rate of 0.17 m/s....
1. Consider the equation below. (If an answer does not exist, enter DNE.) f(x) = e2x...
The equation of a degree 3 polynomial P(x) given that P(0)=1 , P'(1)=3 , P''(2)= -3
4. Find the area of the region bounded by the curve y = 4 − x...
Find the area of the triangular region with vertices : (0,1,0), (2, 1, -1), (1, 2,...
Test the series for convergence or divergence. ∞ en n2 n = 1 convergent or divergent
A spherical tank of radius 10 meters is completely full of liquefied petroleum gas. All the...
If $8000 is deposited at the end of each half year in an account that earns...
Two cars start moving from the same point. One travels south at 56 mi/hr and the...
Determine whether the integral is convergent or divergent. 0 −∞ z z4 + 25 dz If...
7- List three uppercase letters that do not exhibit either reflection or rotation symmetries.
Suppose a cup of coffee is 160 degrees right after the coffee is poured. You are...
A rectangular box must have a volume of 2 cubic meters. The material for the base...
1. Integrate f(x, y) = x + y over the region in the first quadrant bounded...
Consider the function in x,y where f(x,y) = 7.47x2 + 2.47xy + 8.05y. Find the x...
Suppose that the velocity of a rocket shot directly into the air is given by v(t)...
2. Solve the initial-value problem: y′′′ + 4y′ = t, y(0) = y′(0) = 0, y′′(0)...
The distance from the point S(-1, 9, 6) to the line x = -4 + 12t,...
) Use spherical coordinates to find the volume of the solid situated below x^2 + y...
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