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Calculus Questions
A piece of wire 5 m long is cut into two pieces. One piece is bent...
Find the equation of the sphere centered at (2,3,1) that intersects the plane y=8 at a...
(1 point) Evaluate the integral by interpreting it in terms of areas. In other words, draw...
A water trough has a semi circular cross-section with radius of 1 m and a length...
2.1 Calculate the tangent plane to the following surfaces in the given point (a) x2 +...
Use only one substitution ? = ⋯ and show all the stepsto find : [10] ∫...
5. Suppose a sheep has been tied to a small shed that sits in the middle...
1. Integral sin(x+1)sin(2x)dx 2.Integral xe^x dx 3. integral ln sqrt(x) dx 4. integral sqrt(x) lnx dx
Find the maximum rate of change of f at the given point and the direction in...
a)A circular observation window on a cruise ship has a radius of 1 foot and the...
Find the relative maximum and minimum values. f(x,y)=x^3+y^3−24xy
After finding the partial fraction decomposition, ∫ (10x^2−27x−38)/((x^2+4)(x−6))dx = ?dx Notice you are NOT antidifferentiating...just give...
Find the area enclosed by y=4-x^2 and y=x+2
The Fundamental Theorem of Calculus allows the calculation of definite integrals given an integration interval. Not...
Let F(x,y) = x^2 +3xy+4y^2 −14. Solve the equation x^2 +3xy+4y^2 −14 = 0 by the...
A stone is thrown straight up from the edge of a roof, 700 feet above the...
question 01 :Poisson distribution: X~Poisson(lambda=6). Evaluate Pr(X>7) and round to three decimal places. Question 02 :Assume...
Calculating the integral of a function means calculating the area between its curve and the x-axis,...
Consider two spheres, S1 with radius R, S2 with radius r, R > r. The distance...
Suppose the annual revenue of a startup can be modeled by the equation R(t) = (2t)/(t...
Create a function and determine the exact limit at a specific value for x by using...
Define a function f as follows: f ( x ) = sin ( x )...
At what value(s) of x does f(x)=x^4-8x^2 have a local minimum?
Find the volume of the solid obtained by rotating the region bounded by the given curves...
using only words can you explain how to solve: find dy/dx by implicit differentiation. tan^-1 (x^2,y)=x+xy^2
1. The cost function C and the price-demand function p are given. Assume that the value...
Use the Squeeze Theorem for Limits at −∞ to find lim as x→−∞(cosx−x)
A conical container having a top radius of 6 meters and a height of 9 meters...
Use cylindrical coordinates to determine the volume of the solid bound by z = 32 −...
y′′+y′+5y=t−uπ/2(t)(t−π/2); y(0)=2, y′(0)=1. uπ/2 is unit step function starting at π/2
(b)
(1 point) A Norman window has the shape of a rectangle surmounted by a semicircle. If...
Given the parallel planes x + 2y + 3z = 1 and 3x + 6y +...
Set up and evaluate a triple integral for the volume of a cylinder of radius a...
A commercial cherry grower estimates from past records that if 26 trees are planted per acre,...
Use the definition of a Taylor Series to find the taylor series for f(x) = e^(-x/2)...
A rectangular flower bed, bordered by a wall on one side, is to be constructed that...
using the function : (x^2 + (a - 2) x-2a)/(x^2 + (3-5)x-15) a) what value of...
Determine all values which satisfy the conclusion of the MVT for the given function and interval...
Find the volume found by rotating the region between y=x^2, y=sqrt(x), about the line y=1
Find the slope of the tangent line to the curve r = sinO + cosO at...
2.1 Calculate the tangent plane to the following surfaces in the given point (a) x2 +...
Find the domain of the vector function r (t) = <sent, lnt, 1 / (x-2)> a.(0,...
A uniform cable measuring 40 feet is hung from the top of a building. The cable...
Find the angle in degrees between the vectors a = (1,2,2) and b = (3,4,0). Approximate...
Use spherical coordinates to evaluate the following integral, ∫ ∫ ∫ y2z dV, E where E...
A uniform cable measuring 40 feet is hung from the top of a building. The cable...
The planes x + 3 y − 2 z = 1 and 2 x − y...
If the equation dx/dt = f(x, y), dy/dt = g(x, y) has a locally stable equilibrium...
QA: Using by-hand formulas first (and Desmos only to verify later), (i) Find the x values...
Poisson distribution: X~Poisson(lambda=4.5). Evaluate Pr(1≤X<8) and round to three decimal places.
Bruno has a habit of collecting odd bits of “stuff”. While cleaning out his cupboard, he...
Snell's Law at its heart is a minimization problem. Light takes the path which takes the...
Find all local extrema and the intervals on which f(x)=x+sin(2x), considered on the interval (-pi/2,pi/2) is...
Solve the following initial-value problem by using integrating factors: ?2y′ + ?? = 1 , x...
Consider the autonomous first-order differential equation dy/dx=4y-(y^3). 1. Classify each critical point as asymptotically stable, unstable,...
1. Find the general solution of the first order linear differential equation: 2*x*dy/dx -y-3/sqrt(x)=0. sqrt() =...
Find the equations of both the tangent and normal lines to ? = 2? 4 −...
(a) Verify that all members of the family y = (2)1/2 (c - x2)-1/2 are solutions...
For the function f(x)=ax3+bx2-5x+9, determine the values of a and b so that f(-1)=12 and f'(-1)=3
The top of a ladder slides down a vertical wall at a rate of .1 m/s...
Find the second derivative d ^ 2y / dx ^ 2 at t = 0 for...
Find two unit and orthogonal vectors a 〈?, ?, ?〉 and 〈−?, ?, ?〉.
The tetrahedron is the first octant bounded by the coordinate planes and the plane passing through...
Find the equation (in terms of x and y) of the tangent line to the curve...
For the function given below, find a formula for the Riemann sum obtained by dividing the...
Find a complete summation formula for the Taylor series representation of the function f(x) = ln(2x...
A and B are order-n square matrices, which of the following equations is valid? Select one:...
y“-5y’+6y=(2x+1)e^3x+cosx
Find the total mass of the centroid E bounded by the elliptic paraboloids y= 5−4x^2−z^2 and...
Determine how the following lines interact. (x, y, z) = (-2, 1, 3) + t(1, -1,...
Water is leaking out of an inverted conical tank at a rate of 14400.0 cubic centimeters...
10. (6pts.) Show that the derivative of f(x) = 1 + 8x^ 2 is f ‘(x)...
Find the production level that gives maximum revenue if the demand equation is 4x+3p=1200 a. 150...
Let C be the closed, piecewise smooth curve formed by traveling in straight lines between the...
6. (5 marks) Consider the function f defined by f (x, y) = ln(x − y)....
Lawnco produces three grades of commercial fertilizers. A 100-lb bag of grade A fertilizer contains 18...
question number 1: Find the point of inflection of the graph of the function. (If an...
Determine the open intervals on which the graph is concave upward or concave downward. (Enter your...
Find the present value of the income c (in dollars) over t1 years at the given...
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