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Suppose F⃗ (x,y)=〈x^2+5y,7x−3y^2〉. Use Green's Theorem to calculate the circulation of F⃗ around the perimeter of...
Fill in the blanks: 1) An absolute maximum or absolute minimum is called an ______________ 2)...
a cylindrical can holds 250 ml of liquid. Find the dimensions of the can (radius and...
find the exact length of the curve( y=1 - 1/e^x) , 0<x<2. Thanks!
Prepare the finite difference equation set necessary to solve the linear boundary value problem with n=5:...
Find an equation of the plane tangent to the surface x3 - 2y2 + z4 =...
Find the angle, in degrees, between the planes 2x-3y + 6z = 5 and x-2y +...
For each of the given functions f(x), find the derivative (f^−1)′(c) at the given point c,...
Find an equation of the plane tangent to the surface z = 3x2 - 2y3 +...
Solve the differential equation: (?2 ? / ??2 )− 10 ?? ?? + 52? = 0,...
A function f is said to be continuous on the _______ at x = c if...
Find the volume of the solid generated by rotating the region bounded by the graphs of...
(1 point) Convert the following point from rectangular to cylindrical coordinates: (4√2,−4√2,9) (r,θ,z)=
A. (1 point) Find the volume of the solid obtained by rotating the region enclosed by...
Explain why if f is a differentiable function in and on a closed path C and...
(TRUE, FALSE) A matrix multiplied by its inverse is always equal to the identity matrix.
Compute the volume of the solid formed by the region between the graph of f(x)=x+2 and...
A diving pool that is 7m deep and full of water has a viewing window on...
At what point does the graph of y = ln x have maximum curvature?
Evaluate ∫C2x2+y2+1dS where C is the portion of the line segments from the point (1,0) to...
In this problem, p, price, is in dollars and x is the number of units. The...
Choose the correct answer: 1) The curve r = 2 + cos(2θ) is symmetric about Select...
Find the area of the region enclosed by the curve x = 8cos(t) − 4sin(2t), y...
4. Consider the planes x + 2y − 2z = −4 and 2x − 5y −...
Find the radius of convergence, R, of the series. ∞ n = 1 (−1)nxn n2 R...
3. Consider the plane with a normal vector 〈2, 5, −1〉 which contains the point (3,...
Evaluate the following double integral by first converting to polar coordinates: S(2,0)S(sqrt(4-x^2),-sqrt(4-x^2))e^(x^2+y^2)dydx
evaluate the double integral D (xsiny) dA D is bounded by y = 1, y=x, and...
Find the equation of the tangent line to the curve y = 3 sec x -...
A thermometer is placed outside. The initial temperature of the thermometer is 2◦C. After 1 minute,...
Use the Chain Rule to find dz/dt. (Enter your answer only in terms of t.) z...
Use the Laplace transform to solve the following, given the initial conditions: y^'' +5y^'+4y = 0...
integrate ∫(x^2+1)e^-x dx
find the length of the polar curve r=sin^2x. use symmetry and consider only 0 to pie/2
Find the area of the part of the cylinder x2+y2=2ax that lies inside the sphere x2+y2+z2=4a2...
Under ideal conditions, a bacteria population (denoted P) is known to double every 8 hours. Suppose...
Please solve the autonomous differential equation and determine the stability. y' = (y^2 - 4) /...
1. if limit X approaches to 2 from the negative side then evaluate the equation X-10/X-2...
the temperature inside a room is 70F. a termometer has been placed outside of the room,...
. Explain why integral of (g(x) sin(x) dx) is equal to (- g(x) cos(x) + integral...
Let f(x) be defined below. f(x) = { 1 if x < 1 x 2 if...
Find the directions in which the function increases and decreases most rapidly at Upper P 0....
Find T, N, and B for the given space curve. r(t) = (t2-9)i + (2t-9)j +...
Calculate the arc length of the indicated portion of the curve r(t). r(t) = 6√2 t^((3⁄2)...
Evaluate ∮C(x^3+xy)dx+(cos(y)+x2)dy∮C(x^3+xy)dx+(cos(y)+x^2)dy where C is the positively oriented boundary of the region bounded by C:0≤x^2+y^2≤16, x≥0,y≥0C:0≤x^2+y^2≤16,x≥0,y≥0
A dietician is planning a snack package of fruit and nuts. Each ounce of fruit will...
9. Let (x, y) be a point lying on the graph of y=√x. Let d denote...
B. a non-homogeneous differential equation, a complementary solution, and a particular solution are given. Find a...
1) The region bounded by f(x)=−3x^2+18x+21, x=0, and y=0 is rotated about the y-axis. Find the...
Related Rates: The pool is 20m long, and getting longer at a rate of 0.4m/second. The...
For: ?(?)= 2 −4√? 3?6 a. Use exponent rules to rewrite ?(?) to fit the Power...
A box with a square base and open top must have a volume of 364500 cm3cm3....
a) Sketch the graph of r = 1 + sin2θ in polar coordinates with proper explanation....
Use the second derivative to find the intervals where f(x) = x4+8x3 is concave upward and...
Suppose that a cup of soup cooled from 90C to 50C after 25 minutes in a...
1) Differentiate the function y=(4x-4)3(2-x5)3 2) Differentiate the function y=(x+5/x-1)8 3) Find the indicated derivative y=((2t-4)8/t-8)
For f(x, y) = x2 + 4xy - y2 at the point P(2, 1), a) find...
Use logarithmic differentiation to find dy/dx if y = (1/x)tan5x
1. Consider the ODE dy/ dx = tanh(x) − y tanh(x). Use the integrating factor method...
Evaluate each limit. Use l' Hospital's Rule if appropriate. a) limx→−3 81−x^4/9x+27 b) limx→0 e^3x −1−3x/x^2...
Use Laplace Transforms to solve the initial value problem for y(t). Show all steps. Circle your...
Find the four second partial derivatives of f(x, y) = 2x^5y^2 + x^2 y. please show...
Q1) (a) What is the distance of a point (x,y) to the line −2x+4y=−16? The solution...
1. Determine the convergence or divergence of the sequence with given ??h term (a) an=4-5/(n^2+1) (b)...
Create and differentiate a function that involves at least one composition, product, and quotient. Using the...
If u→= (9i+5j+6k), v→= (5i-3j+7k), and w→= (8i+2j+4k), what is the area of the parralelogram determined...
Find the distance from the point <8,−3,5> to the line x=−9−3∗t,y=8−3∗t,z=−4−8∗t
Find the point on the plane curve xy = 1, x > 0 where the curvature...
5. (9 pts) Find the area of the triangle with vertices at (1, 2), (5, 7),...
A 480-lb object is launched from the ground with an initial upward velocity of 70 ft/sec....
1) Use traces to sketch and identify the surface: (?/3)^2+(?/5)^2+(?/9)^2=1 2) Find and sketch domain of...
Evaluate ∂2f∂z∂y∂2f∂z∂y for the function f(x,y,z)=ln(5x2y−2xzy3)
use the method of Lagrange multipliers to find the absolute maximum and minimum values of the...
1. Solve the equation ln(x + 5) − ln(x − 3) = 1 for x. 2.Find...
3. Consider the region R in the first quadrant enclosed by y = x, y =...
a.) Let S be the solid obtained by rotating the region bounded by the curves y=x(x−1)^2...
Determine the volume of the solid generated by rotating the region bounded by the function f(x)=√x,...
Write an equation for the tangent line to to the curve at the given point. Simplify...
for the given initial value problem: (2-t)y' + 2y =(2-t)3(ln(t)) ; y(1) = -2 solve the...
Evaluate ∮C(6y−3y2+x)dx+yx3dy where C is the boundary of the parallelogram with vertices A(−1,−1),B(1,1),C(−1,2) and D(1,4)
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