Calculus question and answers for August 15, 2023
- Q Suppose that a problem grows according to a logistical model with a carrying capacity 6200 and k=0.0015 use Euler's method with a step size h=1 to estimate the population after...
- Q A carpenter is building a rectangular room with a fixed perimeter of 148 ft. What are the dimensions of the largest room that can be built? What is its area?The...
- Q A cylindrical can has a volume of 1024? cm. What dimensions yield the minimum surface area?The radius of the can with the minimum surface area is cm.(Simplify your answer.)
- Q Find the relative maximum and minimum values.f(x,y)=x+y-30xySelect the correct choice below and, if necessary, fill in the answer boxes to complete your choice.A. The function has a relative maximum value...
- Q Two variable quantities A and B are found to be related by the equation given below. What is the rate of change dA/ dt at the moment when A=3 and...
- Q A one-product company finds that its profit, P, in millions of dollars, is given by the following equation where a is the amount spent on advertising, in millions of dollars,...
- Q Find the relative maximum and minimum values.f(x,y) = x + xy + y - 4y +5Select the correct choice below and, if necessary, fill in the answer boxes to complete...
- Q Find the relative maximum and minimum values and the saddle points.f(x,y) = 200y + x-xyFind the relative maximum. Select the correct choice below and, if necessary, fill in the answer...
- Q A flat metal plate is mounted on a coordinate plane. The temperature of the plate, in degrees Fahrenheit, at point (x,y) is given by 3x2 + y-6x+6y. Find the minimum...
- Q A ball is thrown upward from the top of a building. The ball's height above ground at t seconds can be modeled by the equationH(t) = -8t + 40t +...
- Q Find the absolute maximum and absolute minimum values off on the given interval.f(x) = 19 + 2x - x, [0,5]absolute minimum valueabsolute maximum value
- Q This extreme value problem has a solution with both a maximum value and a minimum value. Use Lagrange multipliers to find the extreme values of the function subject to the...
- Q Use Lagrange multipliers to find three positive numbers whose sum is 15 and the sum of whose squares is as small as possible. (Enter your answers as a comma-separated list.)
- Q Use a graph or level curves or both to find the local maximum and minimum values and saddle point(s) of the function. Then use calculus to find these values precisely....
- Q Find the local maximum and minimum values and saddle point(s) of the function. You are encouraged to use a calculator or computer to graph the function with a domain and...
- Q The temperature at a point (x, y, z) is given byT(x, y, z) = 400e^(-x-5y-9z)where T is measured in C and x, y, z in meters.(a) Find the rate of...
- Q Use the Quotient Rule to find the derivative of the function.y = x? / (1 - x?)x? (6 - x?) / (1- x?)6x? / 1-5x?(x? - 1) / (x?(x? -...
- Q Suppose the distance s (in feet) covered by a car moving along a straight road after t seconds is given by the function s = f(t) = 3t + 13t.a....
- Q Find the unit cost (l.e. dollars per unit). Round the answer to 3 decimal places when necessary.Dove liquid body wash costs $5.82 for 16 oz.The unit cost is $ per...
- Q Use a graphing calculator to graph the function.f(x)=2x- 3x-3Use the graph to find the approximate coordinates of the local minimum. Give your answer to 2 decimal places.x=y =Use the graph...
- Q Give the x- and y-intercepts, multiplicities, and end behavior for the polynomial function. Then use the information to identify the graph.h(x) = (x-1) (x+3)There is a negative x-intercept at x...
- Q A man 6 ft tall walks at a rate of 5 ft/sec away from a lamppost that is 14 ft high. At what rate is the length of his shadow...
- Q The one of the function g is defined below.g(x) =5x-3/x+2Find g?(x), where g? is the inverse of g.Also state the domain and range of g? in interval notation.g?(x) =Domain of...
- Q The one-to-one function f is defined below.f(x)=x - 2Find f?(x), where f? is the inverse of f.
- Q Find the equation for the tangent line and the normal line to the graph of the following equation at the specified point.f(x) = (5- 6x + 2x) ; @ (1,...
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