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For the function ?(?) = ?^3 + 3x^2 + 1 determine All intervals where the graph...
Find two positive numbers x and y whose sum is 7 so that x^(2)*y−8x is a...
Consider the vector field. F(x, y, z) = 6ex sin(y), 7ey sin(z), 5ez sin(x) (a) Find...
Evaluate ∫∫R(6xy+4)dA, ∫ ∫ R ( 6 x y + 4 ) d A , where...
Suppose that a printing firm considers its production as a continuous income stream. If the annual...
Find the maximum and minimum values of the function g(θ)=5θ−6sin(θ) on the interval [0,π] Minimum Value =...
Find all local extreme values of the function f(x,y)=2x2−3y2−4xy−4x−16y+1.
The indicated function y1(x) is a solution of the given differential equation. Use reduction of order...
A lifeguard has 1800 feet of rope that she wants to use to create 3 congruent...
Use implicit differentiation to find the second derivative of y at point (1, 8), if y...
I have a question that relates to 14.7 from the Stewart Calculus book regarding absolute max...
(f. 53v) A merchant has 40 marks of silver alloy [one mark is 8 ounces] with...
use the disk method calculate the volume y = 2x , y = x^2 rotate about...
Determine whether the following statement is TRUE or FALSE: The total distance traveled by the particle...
Express the following in cartesian form a+ib . 1/(1+cosx+isinx)
Let f(x,y,z)=yz/x. Use linearization (or differentials) to approximate f(1.01,2.04,2.97)
Two cars start moving from the same point. One travels south at 60 mi/h and the...
For the next two series, (1) find the interval of convergence and (2) study convergence at...
1. Evaluate the Riemann sum for f(x) = 2x − 1, −6 ≤ x ≤ 4,...
The zoo is building a new polar bear exhibit, and wants to put a semi-circular window...
Determine which of the following equations are separable. If it is separable, find its general solution....
The lifetime of a calculator costing $250 is exponentially distributed with mean 3 years. The manufacturer...
A piece of wire 14 m long is cut into two pieces. One piece is bent...
Find the maximal volume of a square based box with the sum of its length, width,...
1) Find the local maximum and minimum values and saddle point(s) of the function. If you...
Consider the function ?(?)=?^3 − 4x^2 + 3? − 2 1) Find the average slope of...
find the volume of the solid enclosed by the two paraboloids y=x^2+z^2 and y=2-x^2-z^2
Let f(x)= x^7(x−6)^8 / (x^2+4)^6 Use logarithmic differentiation to determine the derivative.
Consider the function F(x, y, z) =x2/2− y3/3 + z6/6 − 1. (a) Find the gradient...
Write a triple integral including limits of integration that gives the volume of the cap of...
Find the solution to the separable differential equation dy = x cos2 y + sin x...
1.f(x) = -x^3 -3x^2 +9x-2 Find the value of any relative extreme 2.K(t)=40t/t^2+25 (a) Identify the...
Give a formula for the area element in the plane in rectangular coordinates x and y....
Certain pieces of antique furniture increased very rapidly in price in the 1970s and 1980s. For...
Consider the IVP (x^2 - 2x)dy/dx = (x-2)y + x^2, y(1)=-2. Solve the IVP. Give the...
(a) Show that the function f(x)=x^x is increasing on (e^(-1), infinity) (b) Let f(x) be as...
1) Let a = 2i −4j +4k and b= 7i −6j +6k . Find a⋅b 2)...
I need answers as soon as possible 1.There is a number 61 on a whiteboard. Every...
Find the directional derivative of the function at the given point, in the vector direction v...
Find the intervals where f(x) = (sinx) / (cosx+2), 0 ≤ x <≤2π, is increasing or...
5. In the following exercises solve the given equation using the integrating factor method. Assumet>0: (a)...
Evaluate the flux integral ∫ ∫ S F · n dS. F = 〈8, 0, z〉,...
Find the interval of convergence of the series 1 - 1/2x^2 + 1.3/1.2 x^4 - 1.3.5/1.2.3...
1. find all vertical asymptotes of function f(x) = In((e^2In(x))-5x+6) 2. find all x intercepts of...
A ball is thrown eastward into the air from the origin (in the direction of the...
1. f '(x) = 14x − 20x3; f(3) = 7 2. f ''(x) = x2, f '(0)...
Determine whether Rolle’s Theorem can be applied to ?(?) = 3 − |? − 3| on...
Find the absolute extrema if they exist, as well as all values of x where they...
Solve the initial value problem: y”+16y’+64y=7e^(-t) y(0)=0, y’(0)=0
Consider the differential equation y”+5y’+6y=f(t). Write the form of the particular solution if f(t) is the...
If the infinite curve y = e−6x, x ≥ 0, is rotated about the x-axis, find...
write your complete solution using calculus if the two equal sides of an isosceles triangle have...
A dam is inclined at an angle of 30° from the vertical and has the shape...
Evaluate the limit using the appropriate properties of limits. (If an answer does not exist, enter...
Use Laplace transform to solve IVP 2y”+2y’+y=2t , y(0)=1 , y’(0)=-1
Use Newton's method to approximate the solution to the equation 9ln(x)=−4x+6. Use x0=3 as your starting...
1.) Let f ( x , y , z ) = x ^3 + y +...
9. Solve y′′ − 9y′ + 2y = te^t using the method of Undetermined Coefficients.
Using the Shells method, find the volume of the solid generated by revolving the region bounded...
Sketch a graph of a function having the following properties. Make sure to label local extremes...
Consider a lamina of density ρ = 1 the region bounded by the x-axis, the y-axis,...
Consider the vector field F = <2 x y^3 , 3 x^2 y^2+sin y>. Compute the...
1-Find partial derivative of zx for zcosz=x2y3+z 2- Find tangent plane eq. to the surface zx2+xy2+yz2=5...
1. The linearization of f(x)=(e^x^2) at x=1 is? 2. The linear approximation of f(x)=sqrt(x+3) is? 3....
Find the Maclaurin series expansion for the function. f(x)=e^6x
The supply and demand equations for a product have been estimated to be: S : p...
Consider the integral ∫12 0 (2?^2+3?+2)?? (a) Find the Riemann sum for this integral using left...
Find the Taylor series for f(x) centered at the given value of a. [Assume that f...
5. Solve the Bernouilli equation dx/dx = 5y^2 + 4y/x .
Use the definition of Taylor series to find the first five terms of f(x)=lnx centered at...
Determine the force due to hydrostatic pressure on the flat vertical side of a tank which...
Find the coefficients A(ω) and B(ω) in the Fourier integral of the function f(x) = e^...
Question 3: R(q) = 15q C(q) = 300+15q+0.3q^2+0.002q^3 a) Give an equation for the profit function...
f(x,y) = (x^4-y^2) / (x^4 + y^2). show the following limit does not exist, and explain...
A square tile is expanding as it is heated. Right now, the 16 cm tile is...
Find the parametric equations of the line in which the planes x+2y+4z=1and -2x-2y+z=4 intersect.
1. Use the properties of logarithms to expand the following expression as much as possible. Simplify...
Write the vector , as the sum of a vector parallel to , and a vector...
Calculate the eigenvalues and eigenvectors of the following matrices. B = a11=c, a12=m a21=-m and a22=c...
1. A street light is mounted on top of a 6-meter-tall pole.A man 2 m tall...
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