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Calculus Questions
The function f(x,y)equals2 x squared plus y squared has an absolute maximum value and absolute minimum...
3.Find the four second partial derivatives of z = 2xey - 3ye-x 4.Find the linear approximation...
A rectangular box is to have a square base and a volume of 16 ft3. If...
c. Explain what is wrong with the following statement: ∫ ?(5?)?? = 5 ∫ ?(?)?? d....
Find the volume of a solid (washer type) created by rotating the area between the curve...
Calculate the following; Find the area bounded by the curve ?=2/? between ?=3 and ?=7. Give...
A Norman window has the shape of a semicircle atop a rectangle so that the diameter...
Given f(x)= x3-x2; [-1,2] answer the following questions. a) Find the value(s) of c that satisfies...
a. Find the open intervals on which the function is increasing and decreasing. b. Identify the...
4. A 17 ft long ladder is leaning against a vertical wall. A winch on the...
Find the x coordinate of the point, correct to two decimal places, on the parabola y=6.17-x^2...
1. You are looking to spruce up your garden by making a rectangular enclosure using a...
Use the gradient to find the directional derivative of the function at P in the direction...
Prove that the integral from 0 to Infinity (sin^2(x)e^-x)dx converges using the comparison test.
This is similar to a problem in the textbook. Time (months) 0 1 2 3 4...
Use analytical methods to find all local extrema of the function f(x)=3x^1/x for x>0. The function...
Consider the function below. f(x) = 7 + 4x2 − x4 (a) Find the interval of...
Find a Cartesian equation for the curve and identify it. r = 2 tan(θ) sec(θ)
Start by deriving a recurrence relation giving ?? for ? ≥ 2 in terms of ?0...
Determine whether the sequence a_n = (3^n + 4^n)^(1/n) diverges or converges
The initial speed of a projectile is 1500 ft/sec, fired at the angle of 30 degrees....
Find the arc length function for the curve with the given starting point y=14x3/2,P0(1,14)
Let f(x)=10-2x a.) Sketch the region R under the graph of f on the interval [0,5],...
Find the mass of the triangular region with vertices (0, 0), (3, 0), and (0, 5),...
Determine the region in the xy-plane in which f(x,y)=cos(x2+y2) is continuous.
Find the local maximum and minimum values and saddle point(s) of the function. If you have...
Find the unit tangent vector T and the principle unit normal vector N of ⃗r(t) =...
Calculate ∮c(2?^2 − 3?) ?? + (?+ 2?^2)?? where C is a closed curve (0,0) (2,0) (2,1)...
Minimize Q=2x^2+7y^2, where x+y=9
Use the fifth-degree polynomial for ?(?) = √1 + ? in order to estimate √2.7
Power Series (3 marks total) Find a power series representation and the radius of convergence for...
The circumference of a sphere was measured to be 84 cm with a possible error of...
The function f(x)=2x3−36x2+120x+8f(x)=2x3-36x2+120x+8 has one local minimum and one local maximum. This function has a local...
f(x)= x^3+2x^2-13x+10/x^2-1 Show that the line x= -1 is a vertical asymptote of f, but x=1...
A ball is thrown directly upward from the edge of a rock and travels such that...
5. You are standing in an elevator shaped like a box with a square floor (a...
The management of the UNICO department store has decided to enclose an 886 ft2 area outside...
The owner of the Rancho Grande has 2,996 yd of fencing with which to enclose a...
A tank in the shape of an inverted right circular cone has height 6 meters and...
Find the absolute maximum and minimum values of the function f(x)=12/x−10+3ln(x−10) on the interval [34/3,15] Doesnt...
The function y1(t) = t is a solution to the equation. t2 y'' + 2ty' -...
Let A be the region bounded by the graphs y = 1 √ x , y...
critical numbers 6sin3x(cos3x)-3sin(3x)
determine the equation of the tangent line at point (1,-2) on the curve defined by the...
Let h(x) = f (g(x) − (x^2 + 1)) . If f(0) = 3, f(2) =...
Find all second derivatives of f(x,y)= cos(yx^2). Please show all your work.
Set up the triple integral, including limits, of the function over the region. f(x, y, z)...
The position function of an object moving along a straight line is given by s =...
given:f(x)=x2e-x+5 use 7 intervals from 3 to 7.2 to approximate the area using a.left rectangle b.right...
Find the maximum and minimum values of f(x,y)= xy on the ellipse 9x^2+y^2 = 8.
1)Find sets of parametric equations and symmetric equations of the line that passes through the two...
Evaluate the iterated integral. int from 0 to 1 , int from 0 to x^7 sqrt(1-x^8)...
rectangular tank with a square base, an open top, and a volume of 8788 ft^3 is...
1218) y=Ax+Cx^B is the general solution of the first-order homogeneous DEQ: (x-y) dx - 2x dy...
A company is making a batch of salt water to sell for aquariums. They have designed...
The curves x = sin y and y = (x − 1)^2 + π/2 along with...
f(x) = (sin x)2(cos x)5 a) Find the first derivative of your function in fully factored...
1) Use calculus to find the volume of the solid pyramid in the first octant that...
(a) The population of a city in 2003 was 755932. Assume that the city’s population is...
Find the slope of the line tangent to the function sin(2x)+ x at x = pi/4
A bacteria culture initially contains 40 cells and grows at a rate proportional to its size....
A company plans to manufacture closed rectangular boxes that have a volume of 108 ft^3. Find...
1- Find the solution of the following equations. For each equation, 2- determine the type of...
In the following exercises use the Lagrange multiplier method to find the extremes constrained to the...
1. An oil tanker had an accident, causing a spill in the shape of a circle....
Answer the question with words only, NO equations Find an equation of the plane. The plane...
Find the derivatives of each of the following functions. DO NOT simplify your answers. (a) f(x)...
The volume of a cube is decreasing at the rate of 360cm^3/sec at the moment its...
One airplane is approaching an airport from the north at 201 km/hr. A second airplane approaches...
integrate ∫tan5xsec4xdx (use a pythgorean identity)
Find the average value of f(x, y) = 1/x over the circle in R2 of radius...
Determine the force due to hydrostatic pressure on the flat vertical side of a tank which...
Marginal Cost A division of Ditton Industries manufactures a deluxe toaster oven. Management has determined that...
Calculate the area of the surface of revolution when the function is revolved about the x-axis....
differentiate. a. e^xtan(x) b. sin(1/sqrtx) c. ln(e^x/sqrt(x^2)+3) d. subscriptx tan(x) e. f(secx) where f'(x)= x/ln(x)
Find the area of the largest rectangle with one corner at the origin, the opposite corner...
This problem explores two analytical methods to approximate 4√(16.5) = (16.5)1/4 (a) Calculate the linear approximation...
Given the following Laplace transform functions and input wave-forms, find the output signal. G(s)=(s^2+3s+4)/s(s+1),v in(t)=3sin(2t-0.15)
A 12 foot ladder is leaning against a building. If the bottom of the ladder is...
To illustrate the Mean Value Theorem with a specific function, let's consider f(x) = x^3 −...
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