Calculus question and answers for August 14, 2023
- Q A population of a particular yeast cell develops with a constant relative growth rate of 0.4285 per hour. The initial population consists of 3.5 million cells. Find the population size...
- Q A particle moves with position functions=t^4-4t - 8t + 15t, t? 0(a) At what time does the particle have a velocity of 15 m/s? (Enter your answers as a comma-separated...
- Q Solve the partial differential equation (D - DD' - 2D')z = (2x+xy-y) sin(xy) - cos(xy).
- Q Find f'(x) and find the value(s) of x where f'(x) = 0.f(x) = x/ x^2 +16f'(x) =Find the value(s) of x where f'(x) = 0.x=(Simplify your answer. Use a comma...
- Q Differentiate the following function.f(x) = 5+ 4x + 7 e^x
- Q Which of the following functions passes through the point (0, 10) and satisfies f'(x)=8?
- Q Find the maximum and minimum values of f(x, y, z) = 2x + 5y + 5x on the sphere x + y + z = 1.
- Q Suppose the cost (in dollars) for a company is given by C(x)=200+ 16x +0.02x^2, where x is the number of items produced. Find the marginal cost when 800 items are...
- Q For what value of ? is cot ? undefined?I .0II. 180III. 270
- Q Given that (x, y) = (x+2y)/k if x = -2,1 and y = 3,4, is a joint probability distribution function for the random variables X and Y. Find:a. The value...
- Q Find the equation of the line tangent to the graph of f(x) = (In x)^4 at x = 6.
- Q In 2012, 34.1% of all glass containers were recycled. A beverage company used 400,000 lb of glass containers per year. After recycling, the amount of glass, inpounds, still in use...
- Q At what point does the curve have maximum curvature?y = 5e^x(x, y) =What happens to the curvature as x ? ??k(x) approaches as x ? ?o.
- Q Consider g(w) = - 2e^-2/wDetermine the intervals on which g is concave down.g is concave down on:g is concave down nowhere.Determine the intervals on which g is concave up.g is...
- Q Consider g(y) = 6y(ln( 5y))Determine the intervals on which g is concave down.g is concave down on:g is concave down nowhere.Determine the intervals on which g is concave up.g is...
- Q Consider h(t):=14t^4 + 28/5t and use the Second Derivative Test to address the following prompts.Determine the value and location of any local minimum of f. Enter the solution in (t,...
- Q Consider f(z)=-12 sin z/20-10 cos zand use the Second Derivative Test to address the following prompts.Determine the value and location of any local minimum of f. Enter the solution in...
- Q Consider h(t) = t3(-4+ 5t) + 5 and use the Second Derivative Test to address the following prompts.Determine the value and location of any local minimum of f. Enter the...
- Q Consider g(x) = 6 sin x + 13x on [-?/2 , 3?/2]Determine the intervals on which g is concave down.g is concave down on:g is concave down nowhere.Determine the intervals...
- Q Consider f(x) = - 8 sin x - 16 cos x on [0, 2?].Determine the intervals on which f is concave down.f is concave down on:f is concave down nowhere.Determine...
- Q Consider h(x) = 16 (x - 64)^2/3Determine the intervals on which h is concave down.h is concave down on:h is concave down nowhere.Determine the intervals on which h is concave...
- Q Consider g(w) = 11(w - 9)^4 - 2 - 22(w - 9)^2 and use the Second Derivative Test to address the following prompts.Determine the value and location of any local...
- Q Consider h(y)= -1/5 y + 1/2 y^2 -3/7+7/6y^3h is concave up on:Determine the intervals on which h is concave down.h is concave down on:h is concave down nowhere.Determine the intervals...
- Q Consider g(t) = 2t(7 - t) ^1/3Determine the intervals on which g is concave down.g is concave down on:g is concave down nowhere.Determine the intervals on which g is concave...
- Q Consider h(u) = 6u+2u^4 +4u-7-6uDetermine the intervals on which is concave down.h is concave down on:h is concave down nowhere.Determine the intervals on which is concave up.h is concave up...
- Q Consider f(x) =-7x-20/x-18Determine the intervals on which f is concave down.Consider f(x) =f is concave down on:f is concave down nowhere.Determine the intervals on which f is concave up.f is...
- Q Consider g(w) =- 6w/w + 11Determine the intervals on which g is concave down.g is concave down on:g is concave down nowhere.Determine the intervals on which g is concave up.g...
- Q Consider h(y) = 2y?162 - y and use the Second Derivative Test to address the following prompts.Determine the value and location of any local minimum of f. Enter the solution...
- Q Consider f(x) = 40x + 17x - 14 - 162 and use the Second Derivative Test to address the following prompts.Determine the value and location of any local minimum of...
- Q Consider h(t) = 10t (11^t) and use the Second Derivative Test to address the following prompts.Determine the value and location of any local minimum of f. Enter the solution in...
- Q Consider h (v)=- 5+5v + 3v and use the Second Derivative Test to address the following prompts.Determine the value and location of any local minimum of f. Enter the solution...
- Q Consider f(t) = 1/10 t^5 - 16/3 t^3Determine the intervals on which f is concave down.f is concave up on:f is concave down on:f is concave down nowhere.Determine the intervals...
- Q Consider g(w) = w + 1 / w+6Determine the intervals on which g is concave down.g is concave down on:g is concave down nowhere.Determine the intervals on which g is...
- Q Consider f(y) = - 13y - 4 + 4yDetermine the intervals on which f is concave down.f is concave down on:f is concave down nowhere.Determine the intervals on which f...
- Q Find dy/ du,du/ dx and dy/dxy=u^53 and u=5x^5-4x^4
- Q Let f(x) = cos 4 x. Find all values of c in the interval( ?/8 ,3?/8) such that f'(c) =
- Q For the polynomial below, 2 and 1 are zeros.2f(x)=x-x-8x + 16x-8Express f(x) as a product of linear factors.=
- Q Use Taylor to derive a numerical differentiation formula of the formf (x) = Af(x) + Bf (x-h) + Cf (x-2h) (h>0)that has precision O(h) for f sufficiently regular. What is...
- Q Consider f(z) = - 8z5e3zDetermine the intervals on which f is decreasing.Of is decreasing on:Of is decreasing nowhere.Determine the intervals on which f is increasing.Of is increasing on:Of is increasing...
- Q Consider h(y) = 24y - 12 tan(y) on-7 TT2' 2Determine the intervals on which h is decreasing.Oh is decreasing on:Oh is decreasing nowhere.Determine the intervals on which h is increasing.Oh...
- Q 1011Find all relative extrema of the function f(x) = x-4. Use the Second Derivative Test where applicable.
- Q Find all points of inflection on the graph of the function f(x)= = = = x + 6x
- Q Calculate two iterations of Newton's Method for the function using the given initial guess. (Round your answers to four decimalplaces.)n1NH2f(x) = x - 7? x? = 2Xnf(x)f'(xn)f(x)f'(xn)Xnf(xn)f'(xn)
- Q Estimate the area under f(x) = x on [0,2] using right endpoint approximation given n = 4.A.B.C.D.83SIN 4
- Q If f(x) > 0 on an interval, then f(x) is:concave up on the intervalconcave down on the intervala straight linecannot be determinedA.B.C.D.
- Q An interior designer wants to decorate a newly constructed house. The function f(x) = 36x-150 represents the amount of money he ears per room decoratedwhere x represents the number of...
- Q A rectangular poster is to contain 128 square inches of print. The margins at the top and bottom of the poster are to be 2 inches,and the margins on the...
- Q Find the points on the graph of the function that are closest to the given point.f(x) = x, (0, 3)(x, y) =(x, y) =(smaller x-value)(larger x-value)
- Q Find the length and width of a rectangle that has the given perimeter and a maximum area.Perimeter: 136 meterslengthwidthmm
- Q Find the equation of the tangent plane of function f(x, y) = ?20-3x - 2y at the point (-1, -2).z=Use the equation of the tangent plane to estimate the value...
- Q Find the marginal cost function.C(x) = 175 +0.9xThe marginal cost function is C'(x) =
- Q If f(x)== tan x, which of the equations below describes the average value of f(x) over the interval [0, 2]?(tan (2))+ (tan (0))2-0o (tan (2)) + (tan (0))tan x dx02-0O2...
- Q Assume v(t) = 4t - 16 on the interval [0, 6].What is the total distance that the object traveled on [0, 6]?O 50O 40O 30O 24
- Q Find the equation of the curve that passes through the point (0, 2) and has a slope of 3x-/y at any point (x, y).y = x + 2y = x...
- Q The rate of change in the number of deer, D, within a town is inversely proportional to the number of people, p, living within the town.Write the differential equation to...
- Q Assume that the distance, D, a baseball is thrown is proportional to the force exerted, F.Does it make sense to use differential equations to model the distance thrown?If so, write...
- Q The absolute maximum of f(x) = 2x-3x +3 on [-1,1] isA) 2B) 1C) 3D) OE) 7
- Q If a population of endangered salmon, S(t), starts out with 80 fish and decreases at a rate proportional to 0.02 times the number of fish present each year, write the...
- Q Let h(v) = -15v/v +4Determine the critical values of h. If multiple such values exist, enter the solutions using a comma-separated list.
- Q If the rate of change of Q is directly proportional to Q, and if Q(0) = 100 and Q(4) = 440, find k, the proportionality constant.A. k = 0.370B. k...
- Q Assume that a population P of cheetah on the Savannah of Africa is proportional to the size of an elephant herd, E. Does it make sense to use differential equations...
- Q A lighthouse is located 560 feet from the nearest point P on a straight shoreline. The revolving beacon in the lighthouse makes one revolution every 6 seconds. Find the rate...
- Q Let f(x) = - 8x - 14/xDetermine the critical values of f. If multiple such values exist, enter the solutions using a comma-separated list.
- Q Let g(z) = 8z ln(-4z)Determine the critical values of g. If multiple such values exist, enter the solutions using a comma-separated list.
- Q The function f(x) = In x satisfies the Mean Value Theorem on the interval [1, e] at c =A) 2B) eC) 1/eD) e-1/eE) e-1/2
- Q Let g(u) = u-5/u+19Determine the critical values of g. If multiple such values exist, enter the solutions using a comma-separated list.
- Q Find dy/dx by implicit differentiation.e^x/y = 8x - y
- Q A model for a company's revenue from selling a software package is R = -2.5p +500p, where p is the price in dollars of the software. What price will maximize...
- Q Suppose that for a company manufacturing calculators, the cost, revenue, and profit equations are given by C = 80,000+ 20x, R=300x-x/20,P=R-Cwhere the production output in 1 week is x calculators....
- Q Find the critical point and classify it as a local maximum, local minimum, saddle point, or none of these.f(x, y) = x - 2xy +9y - 80y
- Q The revenue from sales of x units of a product is given by R(x) = 200x-0.01x, and the cost of producing and selling the product is C(x) = 38x+0.01x +...
- Q Find the critical points and classify them as local maxima, local minima, saddle points, or none of these.f(x, y) = (x+y)(xy + 9)(x, y)=________ (smaller x-value)(x, y) =_______ ...
- Q (a) If A is the area of a circle with radius r and the circle expands as time passes, find dA/dt in terms of (b) Suppose oil spills from a...
- Q A model used for the yield Y of an agricultural crop as a function of the nitrogen level W in the soil (measured in appropriate units) isY=KN /25 + Nwhere...
- Q Divide.(-10x+7x-5)(2x-3)Write your answer in the following form: Quotient +
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