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The function g(x)=x^2/3+x is decreasing on the interval: a) (-1,0) b) (-1/3,0) c) (-3/10,0) d) (-8/27,...
Suppose that two boats leave a dock at different times. One heads due north, the other...
Find f. f '(x) = 7/ 1 − x2 , f 1 2 = 1
Your company needs $500,000 in two years' time for renovations and can earn 4% interest on...
Brain weight B as a function of body weight W in fish has been modeled by...
A tank is is half full of oil that has a density of 900kg/m3. Find the...
Find the family of curves orthogonal to y^3 = kx
Find the length of the curve defined by the parametric equations x=(3/4)t y=3ln((t/4)2−1) from t=5 to...
The average value of a function f(x, y, z) over a solid region E is defined...
in a specific city the number of residents infect by corona t weeks after its outbreak...
Find the total distance traveled by a particle according to the velocity function v(t)=−t+7 m/sec over...
Graph f(x)= x3-x2-16x+16/2x2-18 List and mark the vertical and horizontal asymptotes, oblique asymptotes, zeros, and y-...
Find a point c satisfying the conclusion of the MVT for the given function and interval....
Sketch a possible graph of a function that satisfies the conditions: ? (0 ) = 2,...
Evaluate the indefinite integral ∫1/ ((?2−7?2)^(3/2)) ?? where b is a positive constatnt.
find the first partial derivatives of f(x,y) = ln(x^2+2xy+x^2+1)
2. Is the vector field F = < z cos(y), −xz sin(y), x cos(y)> conservative? Why...
Sketch and then set up the integral for the volume of revolution of the region bounded...
I know that sequence cos(1/n) is bounded but how to show that the sequence {cos(1/n) is...
A body was found in the basement of the Underwater Basket Weaving Building at 12:00 noon...
Determine whether the shapes given below are always, sometimes, or never similar. Briefly explain your answers....
What do Executives and Information Technologists have in common? They are among the worst when it...
Evaluate the line integral by the two following methods. (xy dx + x2 dy) C is...
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...
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