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Explain why the mean value theorem applies to f(x)=3x^2 defined on [-2,1]. Find c that satisfies...
Solve the initial value problem x' = [ 0, 1; -2, 3]x + [0, e^t], x(0)...
Solve the following differential equations. A spring has a constant of 4 N/m. The spring is...
Given the second order initial value problem y′′+25y=5δ(t−1), y(0)=2, y′(0)=−10y″+25y=5δ(t−1), y(0)=2, y′(0)=−10Let Y(s)Y(s) denote the Laplace transform of yy. Then...
Suppose that the demand of a certain item is x=100e−0.02px=100e−0.02p. Evaluate the elasticity at 40: E(40)E(40)...
As a large cube of ice melts at a rate of 5 cubic inches per minute,...
Use Lagrange Multiplier to find the maximum and minimum of f(x,y) = 4x^2 - 4xy +y^2...
∫(8x^3)/sqrt(25+1x^2)dx side A= 1x side B= side C= 1x/5= 1/5dx= dQ sqrt(25+1x^2)/5= 2) Determine the derivative...
Find the Maclaurin polynomial (c = 0) of degree n = 6 for f(x) = cos(2x)....
The system of differential equations dx/dy = 0.4x − 0.004x2 − 0.001xy dy/dt = 0.6y −...
(a) find the elasticity of the demand function q = (15000) / (p^2 + 50) when...
solve a and b please! a) Find the elasticity of the demand function q = 15000...
Evaluate ∫ C 2 xyz d x + x^2 z dy + x^2 y d z...
Find the interval of convergence of Sigma∞ n=1 ((2x−4)^n)/n . Identify the radius R and center...
Solve the initial-value problem. x2y' + 2xy = ln(x), y(1) = 7. Please show all work neatly,...
Find the set of parametric equations of the line through the point (-3,6,3) that is parallel...
(a) (3 pts) Show that f(x) = 4x3 on [0,1] is a probability density function. (Hint:...
A piece of wire 10 m long is cut into two pieces. One piece is bent...
A bus stop shelter has two square sides, a rectangular back and a rectangular roof only...
As a large cube of ice melts at a rate of 5 cubic inches per minute,...
Suppose that f(x)=4x2ln(x),x>0.f(x)=4x2ln(x),x>0. (A) List all the critical values of f(x)f(x). Note: If there are no...
The number ofdefectives in 10 different samples of a 100 observation each is following 1,2,1,0,2,3,1,4,2,1. What...
A glass enclosure is to be made that is in the shape of a half cylinder...
Suppose f is a differentiable function of x and y, and g(u, v) = f(eu +...
For the given function, find all values of c over the interval ( 4 , 6...
Calculate the number of the real roots for f ( x ) = 33 x^ 5...
Calculate the number of real roots for f ( x ) = 5 x ^3 +...
2. Use the product rule for differentiation to find derivatives in each of the following: (a)...
A rectangular box with a square base has a volume of 4 cubic feet. The material...
Assume the demand function is D(x)= -0.6x2+160 and the supply function is S(x)= 0.4x2 +x+50 find...
Using rectangles whose height is given by the value of the function at the midpoint of...
Joey is editing an picture. The picture is a rectangle with a height that always stays...
use Rolle"s theorem to prove that 2x-2-cosx=0 has exactly one real solution
The current toll for the use of a certain toll road is $50. A study conducted...
5.) a.) Integrate G(x,y,z)=xz over the sphere x2+y2+z2=9 b.) Integrate G(x,y,z)=x+y+z over the portion of the...
approximate the area under the curve y=12x-4x2 between x=0 and x=2 using four rectangles of the...
Compute the surface area of the surface generated by revolving the curve ?(?)=(?,??)c(t)=(t,et) about the ?-x-axis...
5. The planes: 2x − 3y + z = 1 and 3x − 2y − z...
Find f. 1.) f '(x) = 1 + 3sqrt(x) , f(9) = 68 2.)f ''(x) =...
Find the most general antiderivative of the function. (Check your answer by differentiation. Use C for...
The owner of a luxury motor yacht that sails among the 4000 Greek islands charges $408/person/day...
Suppose you are climbing a hill whose shape is given by the equation z = 1000...
Find the power series expansion for f(x) = x^2 e^(x^2) centered at a = 0 and...
1. Find the derivatives of each of the following functions: (a) ?(?)=5?3−7?2−9?+√5 (b) ?(?)=3?-4+6√? (c) ?(?)=6/?4−7/?3+3/?+1
Use polar coordinates to find the volume of the solid below the paraboloid z=144−4x^2−4y^2 and above...
Approximate the area under the curve y = 12x−4x2 between x = 0 and x =...
Water leaks from a tank at a rate of 115−2?2‾‾‾‾‾‾‾‾√115−2t2 liters/ hour, where ?t is the...
Suppose that S(x)=∫x0 sin(t5)dt 1. Compute S(0) 2. Compute the derivative S ′(x) 3. Evaluate lim...
A particular computing company finds that its weekly jprofit, in dollars, from the production and sale...
A cylindrical oil drum is to be designed so that its height plus the diameter of...
1)We invest $50 per month in an account that pays 3% interest per year compounded continuously....
Find the equation of the tangent line to the graph of the function f(x)=(x^2+8)(x−2) at the...
Evaluate the integral: ∫23√x2−4x4dx (A) Which trig substitution is correct for this integral? x=4sec(θ) x=4tan(θ) x=23sin(θ) x=2sec(θ)...
A model for the surface area of a human body is given by S = 0.1091w^0.425...
Assume that the strength of a long object like a tree trunk or a steel beam...
Compute the following limits and show all your work: (a) A = lim x→∞ [3x^2 −4/x^2...
Consider the function f(x)=4x2-x3 provide the graph the region bounded by f(x) and the x-axis over...
solve the ODE solving for the general solutions y''+y'-12y=sin(t)e^(3t)
Suppose that ff is a Riemann integrable function on [0,2][0,2] and that ∫20f(x)dx=5∫02f(x)dx=5. Suppose further that...
suppose you have a cardboard of area 36sqrt(3)m^2 and you need to make a triangular prismatic...
Sketch the region enclosed by x = 56 − y^ 2 and x = − y...
Suppose that f(4) is continuous and f′(c) = f′′(c) = f′′′(c) = 0, but f(4) is...
solve the linear order y' - 2y = cos(3x). solve for y.
solve the separable differential eq. y'=(y-3)(y+2)/(x-2)(x=4). solve for y.
A cylindrical can is built to store a food. This can is constructed without a lid...
1. Find the limit as n goes to infinity of xn over n factoiral.
Identify any extrema of the function by recognizing its given form or its form after completing...
Assume the acceleration of the object is a(t) = −32 feet per second per second. (Neglect...
Suppose you deposit $2000 at 4% interest compounded continously. Find the average value of your account...
A function f, a closed interval [a, b], and a number of equally spaced subintervals n...
Find the Taylor Series of the given function centered at the indicated point. x^4 at a...
A 50-foot ladder is placed against a large building. Unfortunately, the base of the ladder is...
Draw an oriented curve C and a vector field F along C that is not always...
find all values of a such that distance from (1,2,a) to the xy-plane equals distance from...
Find the Taylor Series at a=pi/2 for f(x)=5cos(x).
write and evaluate the triple integral for the function f(x,y,z) = z^2 bounded above by the...
Parametrize the curve r(t) = <5sin(t), 5cos(t), 12t> with respect to arc length, measured from the...
Change from rectangular to cylindrical coordinates. (Let r ≥ 0 and 0 ≤ θ ≤ 2π.)...
A Pyramid is 655 ft high (due to erosion, its current height is slightly less) and...
A cyclist leaves her house at 8:00AM and begins travelling directly east at 20 km/h. Fif-...
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