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Calculus Questions
Use the Chain Rule to find dz/dt. (Enter your answer only in terms of t.) z=sqrt(1+x^2+y^2),...
# 12 In Exercises 9–12, determine whether Rolle’s Theorem can be applied to f on the...
A rectangular storage container with an open top is to have a volume of 10 m3....
Suppose a, b and c are the direction angles for the vector . If a =...
Write down the trigonometric and exponential expressions of the following complex a) -2 b) 1-cosΘ +isinΘ...
Let g(u, v) = f(u 3 − v 3 , v3 − u 3 ). Prove...
Find the solution to the following equation using an appropriate integrating factor. Include largest interval solution...
Find all critical values for the following function. Use the first derivative test with a sign...
Find the area of the region that lies inside the first curve and outside the second...
On a certain clock the minute hand is 12 in long and the hour hand is...
F · dS for the given vector field F and the oriented surface S. In other...
a) On a planet where the acceleration due to gravity is given by a(t) = -8m/s^2,...
Find the dimensions (i.e. length, width, height) of a box (with a top) that has a...
sketch graph of a function that continuous on [1,5] an absolute minimum value at x=4 an...
1. The absolute maximum value of f(x) = x 3 − 3x 2 + 12 on...
Find this integral using Integration By Parts; use the Tabular D.I. method. ∫ e^(5x) cos x...
Your underground used-book business is booming. Your policy is to sell all used versions of Calculus...
Find the volume of the solid generated by revolving the region bounded by x2−y2=16, x≥0, y=−4,y=4...
a. *If y=x3+7/x^2/3 , then find dy/dx . Make sure your answer is fully simplified. b....
A fence is to be built to enclose a rectangular area of 280 square feet. The...
let the equation F(16) = -16t^2 + 128t +25 represent the height in feet of a...
6. Given the velocity and initial position of a body moving along a coordinate line at...
A boat is pulled into a dock by means of a rope attached to a pulley...
Evaluate the double integral for the function f(x, y) and the given region R. f(x, y)...
Suppose that 3 J of work is needed to stretch a spring from its natural length...
Find an equation of the tangent plane to the parametric surface r(s,t)=4scos(t)i+3ssin(t)j+5tk at when s=4 and t=3π/4...
In this problem, p is the price per unit in dollars and q is the number...
D(x) is the price, in dollars per unit, that consumers are willing to pay for x...
A tank in the shape of a right circular cylinder, with a height of 15m and...
Find dy/dx if y= (x^3+5x)(4x^2+10)^9
Solve y'-3y=2e^t y(0)=e^3-e using Laplace transform.
1. Consider the function f(x) whose second derivative is f″(x)=10x+2sin(x). If f(0)=2 and f′(0)=3, what is...
please I want the solution of this equation: Calculate the maximum and minimum values of a...
Find the area between the following curves. x=-1, x=2, y=ex, and y=5-ex
The function f(x) = 3x 4 − 4x 3 + 12 is defined for all real...
The base of a solid is the region enclosed by y=sin(x), y=0, x=pi/4 and x=3pi/4. Every...
find f"(x) for f(x) = 1 -2x / 4x+5
please show the work for computing the area of the region bounded by the curve provided...
Maloney’s Marker Company specializes in making green and purple markers. Let x be the number of...
Use the definition of the definite integral to evaluate Integral from 2 to 6 left parenthesis...
Find the area of the region bounded between the functions f(x)= x2 – 2x + 2...
Find the minimum value of the average cost for the given cost function on the given...
Find the equation of the tangent line to the graph of y = e x 2−1...
laplace transform y''+y = cos(2t) y(0) =1 y'(0) = -4
Write a polar equation of a conic with the focus at the origin and the given...
You are given that the function f(x,y)=8x2+y2+2x2y+3 has first partials fx(x,y)=16x+4xy and fy(x,y)=2y+2x2, and has second...
Set up the definite integral(s) that represents the area between the curves y = x2 -...
1. (24 pts.) For which integer values of the constant k does the sequence {a1, a2,...
Air Pollution The amount of nitrogen dioxide, a brown gas that impairs breathing, present in the...
Find an equation for the hyperbola that satisfies the following conditions. Vertices (−1,1) and (1,1); foci...
Consider the parametric equations x = 5 - t^2 , y = t^3 - 48t a....
Find the fundamental vector product. 1. r(u, v) = (u 2 − v 2 ) i...
1.Determine the producer's surplus for the given supply function and demand level x. (Round your answer...
a) Find the length of the curve given by the parametric equations ? = ? ???...
Consider the vector field. F(x, y, z) = 7ex sin(y), 7ey sin(z), 8ez sin(x) (a) Find...
A company needs 150,000 items per year. It costs the company $720 to prepare a production...
20. A piece of land is shaped like a right triangle. Two people start at the...
14. Which value of x, with −4 ≤ x ≤ 4, corresponds to the global (absolute)...
Suppose that c(x)=4x^3-32x^2+18000x is the cost of manufacturing x items. Find a production level that will...
What is the Integral from sqrt2/3 to 2/3 (dx/(x^5sqrt(9x^2-1))
a) If g(x) = x3−6x2 −15x + 7, find the interval(s) on which g is increasing/decreasing,...
Solve the homogenous equation subject to the indicated initial using substitution x = vy. (y3+2x2y)/(2x3) =...
Find the general solution to the differential equation t^2y'' - 2ty' + 2y = 4
Show that 1^3 + 2^3 + 3^3 + ... + n^3 is O(n^4). The proof is
Find ∫ ∫ ∫ E z d V , where E is the solid tetrahedron with...
Sketch the curve. r = 4 + 2 cos(θ) and find area enclosed by it.
The radius of a cylinder is increasing at a rate of 3cm/min while the height is...
Find the area of the region bounded by the two functions f(x) = x^2 − 4x...
Set up integrals for both orders of integration. Use the more convenient order to evaluate the...
What is the difference between derivatives and anti-derivatives and giving an example of each.
A fence is to be built to enclose cows in a rectangular area of 200 square...
A biologist must make a medium to grow a type of bacteria. The percentage of salt...
Find the amount necessary to fund the given withdrawals. Quarterly withdrawals of $530 for 5 years;...
⦁ Find the area enclosed between the x-axis and the curve y=x(x-1)(x+2)
The sales of a new high-tech item (in thousands) are given by S(t)=101-80e-0.2t where t represents...
The enrollment at a local university was 10,000 in 2015 the base year and is 13,500...
The Cobb-Douglas production function for an automobile manufacturer is f(x, y) = 100x0.6y0.4, where x is...
Evaluate s(t)=∫t−∞||r′(u)||dus(t)=∫−∞t||r′(u)||du for the Bernoulli spiral r(t)=〈etcos(4t),etsin(4t)〉r(t)=〈etcos(4t),etsin(4t)〉. It is convenient to take −∞−∞ as the lower...
Question IV: A. For the vector field ?(?, ?, ?) = (? + ?)?⃗ + (?...
A traffic engineer places a camera 20 meters from a highway. The camera will follow any...
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