Calculus question and answers for August 16, 2023
- Q The population of trout in a pond is given by P = 0.4P(1 - P 10,000) -f, where f trout are caught per year.Consider the case where a certain number...
- Q 4. Solve the initial-value problemy"(t)- y'(t)- 6y(t) = 0, y(0) = 2, and y'(0) = 1.[Hint: First determine the solution by computing the roots of the associated quadratic equation, then...
- Q Consider the first-order equation with initial conditiondy/dt=-y+t y(0) = 1Use a value of Ax = h = 1.0 to find y(1) by the third-order Runge-Kutta...
- Q Find the general power series solution centered at Xo= 0 for the differential equationy' - 2xy = 0
- Q Determine the open intervals on which the graph of f(x) = 3x +7x-3 is concavedownward or concave upward.concave downward on (-?,?)concave upward on (-?,0); concave downward on (0,?)concave upward on...
- Q Determine all solutions to the equation -?2sin 2x = sin x + cosx on the interval [0, 2?).x= 5?/8,7?/8x=5?/4,7?/4x=5?/8,7?/8,13?/8,15?/8x=5?/4,7?/4,9?/4,11?/4
- Q Suppose the position equation for a moving object is given by s(t) = 3t + 2t + 5, where s is measured in meters and t is measured in seconds....
- Q Locate the absolute extrema of the function f(x) = x-12x on the closed interval [0, 4].absolute max: (2, -16); absolute min: (4, 16)no absolute max; absolute min: (4, 16)absolute max:...
- Q Suppose the monthly total revenue for the manufacture of golf balls is R(x) = 1.78x, where x is the number of golf balls sold each month.a. What is the slope...
- Q Graph the function. Estimate the intervals on which the function is increasing ordecreasing and any relative maxima or minima.f(x)=7-lx|Determine on which interval(s) f(x) is increasing. Select the correct choice below...
- Q Find an equation of the tangent plane to the surface z = ln(x - 2y) at the point (3, 1,0).
- Q The population of a certain city was 170000 in 1998, and the observed relative growth rate is 3 percent per year. Hint: This model is similar to A=Pe^(rt).(a) Find a...
- Q Consider the function f(x) = -4 ln(x + 3) - 7. Show all work to answer the following:a) What is the parent function?b) List all transformations.c) What is the equations...
- Q Sketch the slope field of y' = y and sketch the solution with initial condition y(0) = -1.
- Q If you deposit $4000 into an account earning 3% interest per year compounded continuously, how long will it take to triple your investment? Show all work and leave your answer...
- Q The height h in centimeters of Shuntaro's pogo stick from the ground as he jumps on it since s seconds have passed is roughly modelled by the equationh(s) = sin2...
- Q An open rectangular box having a volume of 108 in.3 is to be constructed from a tin sheet. Find the dimensions of such a box if the amount of material...
- Q The Ace Novelty company produces two souvenirs: Type A and Type B. The number of Type A souvenirs, x, and the number of Type B souvenirs, y, that the company...
- Q Solve the linear programming problem.MaximizeP=7x+7ySubject to2x+y ? 20x + 2y ? 16x, y ?0Select the correct choice below and fill in any answer boxes present in your choice. Whatis the...
- Q Production Function for a Company: Suppose the production output of a certain country is given byf(x, y) = 100x^3/5.y^2/5billion dollars if x billion dollars are spent for labor and y...
- Q For the function shown in the figure below, find the average rate of change from (-3, 10) to (1, -6).The average rate of change is (Simplify your answer.)
- Q Use the method of Lagrange multipliers to maximize the function subject to the given constraint.Maximize the function f(x, y) =? y - x^2 subject to the constraint x + 2y...
- Q Find the common ratio for the geometric sequence.-1 3, -1 15, -1 75, - 1 375, -1 1875,...Common ratio:
- Q Find the domain of the function. (Enter your answers using interval notation.)g(r, s) = ?rsThe domain of g is the set of all ordered pairs (r, s) such that r...
- Q If f(x) and g(x) are differentiable functions for 0?x?1 such that f(0) = 2, g(0)=0, f(1) = 6, g(1)=2, then which of the following are true for some 0 <c<1(c...
- Q A culture of bacteria has an initial population of 12000 bacteria and doubles every 6 hours. Using the formula P? = P? * 2?/?, where P? is the population after...
- Q Let g(x, y) = cos(x + 2y).(a) Evaluate g(2, -1).g(2, -1) =(b) Find the domain of g.-1 ? x ? 1, -1 2 ? y ? 1 2R-? 2 ?...
- Q Find the derivative of the functionf(t) = arccsc(-t)f'(t) =
- Q Calculate the Taylor polynomial T3 centered at a = a for the given function and values of a and Estimate the accuracy of the 3th degree Taylor approximation, f(x) 73(x),...
- Q Differentiate f and find the domain of f. (Enter the domain in interval notation.)f(x) = In(x - 6x)derivative f'(x) =domain
- Q The governing differential equation is the 1-D heat equation:?T/?t = ?(?T/?x)Using the explicit and implicit methods, determine the finite difference approximations of the differential equation of 1-D heat equation using...
- Q Find the minimum value of f(x,y,z) = x + y + z subject to 8x + 2y + 6z = - 104.The value of f at the minimum is .(Simplify...
- Q Warning: Questions 2 and 3 below are asking for the taylor polynomials centered at x = 1. This means you are plugging x = 1 into the derivatives and including...
- Q Consider the function f(x) = 3 - 3x, -4 ? x ? 2.The absolute maximum value isand this occurs at x equalsThe absolute minimum value isand this occurs at x...
- Q Let f(x) = x?(x - 1).(a) Find the critical numbers of the function f. (Enter your answers from smallest to largest.)smallest value x?=x?=largest value x?=(b) What does the Second Derivative...
- Q Consider the functionf(x) = 2x + 24x - 54x +9 with -9 ? x ? 2This function has an absolute minimum at the pointand an absolute maximum at the point
- Q Consider the function f(x) = 12x? + 30x? - 300x + 2.f(x) has inflection points at (reading from left to right) x = D, E, and Fwhere D isand E...
- Q A cylinder is inscribed in a right circular cone of height 7 and radius (at the base) equal to 4. What are the dimensions of such a cylinder which hasmaximum...
- Q f(x) = 4x/ x - 49(A) List all critical numbers of f. If there are no critical numbers, enter 'NONE'.Critical numbers =(B) Use interval notation to indicate where f(x) is...
- Q For the equation given below, evaluate y' at the point (2, -1).2xy - 3x = -28.y' at (2, -1) = 7/6
- Q Here is a graph of the function h. Use the graph to find the following.If there is more than one answer, separate them with commas.(a) All values at which h...
- Q Suppose the temperature at a point in a metal cube is given by T(u, v, w) = 90 - 55e ^[-1/20(u+v +w)] where the centre of the cube is taken...
- Q The graph of the derivative f' of a function f is shown.(a) On what intervals is f increasing? (Enter your answer using interval notation.)On what intervals is f decreasing? (Enter...
- Q At what rate is the shadow of a 6-ft tall man shortening as he walks at 8 ft/s on a level path toward the streetlight that is 20 ft above...
- Q consider the following graph(a) Find the interval(s) on which f is increasing. (Enter your answer using interval notation.)(b) Find the interval(s) on which f is decreasing.(Enter your answer using interval...
- Q Use the Taylor series to estimate f(x) =(x-1) e^-x at xi+1=1 for Xi = 0.5. Use the 3rd order approximation and calculate the percentage relative true error for each step.
- Q Find the equation of the normal and tangent line to the curve y = 3x - 2x + 1
- Q A 2 m tall woman is running at a rate of 2 m/s when she spots a bird in a tree 6 m off off the ground.How fast is the...
- Q Enzo needs to construct two electrical poles 30 m apart. The first pole is 28 m tall, while the second is 12 m tall. In order to support the weight...
- Q If f(x) = 4x-3x + 3, find f '(0). Use this to find the equation of the tangent line to the parabola y = 4x - 3x + 3 at...
- Q Finance. Suppose that $2,300 is invested at 3.6% annual interest rate, compounded monthly. How much money will be in the account in (A) 6 months? (B) 7 years?(A) Amount after...
- Q Find the equation of the tangent line to the curve y = 8 sinx at the point (?/6,4).The equation of this tangent line can be written in the form y...
- Q Find the following using the table below.if h(x) = f(g(x)) then h'(3) =
- Q Determine the global minima and maxima of the function: (x, y, z) = e^x? +z?under the set:A := {(x, y, z) ? R : x? + (y + z) =...
- Q At Technodynamics, Inc., a randomly-selected hiring committee of 4 people is formed from a group of 4 employees in marketing and 7 employees in management.a) Find the probability that the...
- Q A lottery involves 28 numbers, from which 5 are randomly selected without replacement. Order does not matter.a) How many possible tickets can be played?b) What is the probability that one...
- Q Let I(t) = t - 4t + tand y(t) = t - 3t + 3At t = 1.x(1) =y(1) =dx/dt |t=1 =dy/dt |t=1 =dy/dt |t=1= tangent slope =speed (1) =
- Q The table provides various values, including all zeros, of a tangent function f (x) on the interval [-?, ?].What is the period of the function?
- Q If two lines have no points of intersection and the same direction vector, they are:a. intersecting linesb. skew linesc. parallel linesd. coincident lines
- Q Let F(x) = f(x?) and G(x) = (f(x))?.You also know that a? = 8, f(a) = 2, '(a) = 10, f'(a?) = 9Then F'(a) =and G'(a) =
- Q Find the 30th derivative of the function f(x) = cos(x).A) sin(x)B) -sin(x)c)-cos(x)D) 0E) cos(x)
- Q The probabilities of events E, F, and E?F are given below. Find (a) P(EIF), (b) P(FIE), (c) P (EIF'), and (d) P (FIE').P(E) = 0.4, P(F) = 0.7, P(E?F) =...
- Q The function graphed above is:Increasing on the interval(s)Decreasing on the interval(s)
- Q A bike shop uses two manufacturing plants, one in region A and the other in region B, to build its bicycles. Twice as many bicycles are built in region B...
- Q Consider the function f(x) = 2x - 6x +4, 0 ? x ? 7.The absolute maximum of f(x) (on the given interval) is at x =and the absolute minimum of...
- Q A railroad track and a road cross at right angles. An observer stands on the road 70 meters south of the crossing and watches an eastbound train traveling at 60...
- Q Of the entering class at a college, 75% attended public high school, 16% attended private high school, and 9% were home schooled. Of those who attended public high school, 15%...
- Q The function f(z) = 2x 39x + 180x 7 has two critical numbers.The smaller one is x =and the larger one is x =
- Q Find the equation of the tangent line to the graph of f(x) = 1/x? when x = 1.
- Q The position of a particle moving along the x-axis is x(t)=sin(2t)-cos(3t) for time t?0.When t=?, the acceleration of the particle isA) 1/9B) 9C) -9D) -1/9E) 0
- Q Given the vector field F(x, y) = (ye^sinx cosx, e^sinx) and the curve C with equation y -?ysin x = 0a) Show that F is conservative and find a potential...
- Q Flight of a Rocket The altitude (in feet) of a rocketts into flight is given bys-f(t) =-t +54t + 470t +6 (t ? 0).Find the point of inflection of the...
- Q Determine the point(s) at which the function f(x) = 2x - 15x + 36x has a horizontal tangent line.
- Q A ball is projected upward from the ground. Its distance in feet from the ground in t seconds is given bys(t)=-16t^2+128t. At what times will the ball be 219 feet...
- Q Find the relative maximum and minimum values.f(x,y) = x + xy + y-22y + 161Select the correct choice below and, if necessary, fill in the answer boxes to complete your...
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