Calculus question and answers for August 18, 2023
- Q In Exercises 1-16, calculate the Taylor polynomials T2 and T3 centered at x = afor the given function and value of a.1. f(x) = sin x, a = 02.f(x) =...
- Q $856We found that the marketing research department for the company that manufactures and sells memory chips for microcomputers established the following price-demand and revenuefunctions:p(x) = 85-3xPrice-demand functionRevenue functionR(x)=xp(x) = x(85-3x)where...
- Q Solve each of the following systems using elementary operations:b. 1 2x + 5y = 193x + 4y = 112a. 2x - y = 112 x + 5y = 11c.1(2)-x +...
- Q Consider the following vectors:[][o]Which of the following statements are true? (select all correct answers)Vector x lies in the plane spanned by v and w.uVector w lies in the plane spanned...
- Q (c) If the temperature is 25F, what wind speed makes it feel like 10F?Round your answer to one decimal place.The wind speed is 22.5mph.
- Q Solve the heat conduction problem: ?u/?t = k ?u/?x using NUMERICAL METHOD.Subject to the boundary condition u(0,t) = 0, u(2,t) = 3t + 2 and initial condition u(x,0) = x/2....
- Q Find the rate of change of f(x) = x + 2x - 3 on the interval [1, a].
- Q The rth term of a progression is R, the sth term is S, and the tth term is T.(a) Show that, if the sequence is arithmetic, R(s - t) +...
- Q Calculate the producers' surplus for the supply equation at the indicated unit price p. (Round your answer to the nearest cent.)p = 10 + 2q; D = 36$ ________
- Q Use a graphing utility to graph fand its second-degree polynomial approximation P? at x = c.f(x) = 25/?x, c = 1P?(x) = 25 - 25/2(x - 1) + 75/8(x -...
- Q In your own words, define the following.a. Rate of changeb. Average Rate of ChangeHow do you find the average rate of change?
- Q Find the rate of change of f(x) = x - 2?x on the interval 1 ? x ? 9.
- Q Use the power series for f(x) = arctan(x) to approximate the value, using RN ? 0.001. (Round your answer to three decimal places.) arctan(1/4).
- Q Find the center and radius of the circle given by the equation:x^2 + y^2 + 6x 4y - 12 = 0.
- Q What are the fourth roots of 6 + 6?3i ?Enter your answer by filling in the boxes. Enter the roots in order of increasing angle measure.
- Q For the function f(x) = -6x - 5x - 1, find the equation of the tangent line at x=8.
- Q Calculate the consumers' surplus at the indicated unit price p for the demand equation. (Round your answer to the nearest cent.)q = 130 - 2p; p = 19$ _________
- Q Use a linear approximation (or differentials) to estimate the given number. (Round your answer to five decimal places.)3?126
- Q Find the rate of change of f(x) = x^2 - on the interval 1 ? x ? 2.Find the rate of change of f(x) = x^2 + 4x + 2...
- Q Suppose sin?= 3/5, sin?= 20/29. Moreover, suppose ? is quadrant IV and ? is in quadrant II.Find the following.sin( ?+ ?) =143/145cos(?+ ?)= 24/145
- Q A particle moves along a hyperbola xy 12. As it reaches the point (6,2), the y-coordinate is decreasing at a rate of 4 cm/s. How fast is the x-coordinate of...
- Q The rate of water flow R(!) can be approximated by Q(t) = 1/79(768 + 23t - t)Use Q(t) to approximate the average rate of water flow during the 24-hour time...
- Q What is the exact value of tan (?/12)?-(2-?3)-(2+?3)2-?32+?3
- Q A particle moves along the x-axis with acceleration given by a(t)=sin(t).(a) ?a(t) dt(b) Find the velocity function for the particle if v(O)=3.(c) Find the position function for the particle if...
- Q If c = -0.477, simplify the expression cos(cos-'(c)). If undefined, enter . Provide your answer below:
- Q A three-sided fence is to be built next to a straight section of the Aterno-Pescara river, which forms the fourth side of a rectangular region, as shown in the diagram....
- Q What is the average value of f(x), between x = 1 and x = 5 for f(x) = 4? + 1?
- Q Determine the equation of the tangent line to the curve, y =e^4x/x^3 at x = 1. Use exact values.
- Q Consider the function f(x) = 1 3x, -5?x? 2.The absolute maximum value is and this occurs at I =The absolute minimum value is and this occurs at I=
- Q R is the region bounded by the functions f(x) = 9/(-1+x) and g(x) = x 9. Find the area of the region bounded by the functions on the interval [8,...
- Q Determine the intervals on which h is continuous. Enter the solution using interval notation.h(x) = /11 - 2h is continuous on _____
- Q For the function z= -4x - 2y - xy, find ?z/?x , ?z/?y , ?z(5,1)/?x , and ?z(5,1)/?y
- Q If we apply Rolle's Theorem to the function f(x) = 2x - 8x - 1 on the interval [0, 4], how many values of c exist such that f'(c) =...
- Q Mohamed has a spherical balloon that has a diameter of 10 centimeters. Toby has a spherical balloon that holds 3 times as much air as Mohamed's balloon. What is the...
- Q The function f(x)=7x + 5 is one-to-one.a. Find an equation for f^-1, the inverse functionb. Verify that your equation is correct by showing that f(f^-1(x)) = x and f^-1(f'(x))= x
- Q A ball is thrown directly upward. Its height (in feet) after t seconds is given byy = 80t - 16t^2, for t ? 0.19) ________What is the maximum height in...
- Q Write the ratios for sin A and cos A.A right angle triangle in which h = 26, p = 10 and b = 24.
- Q Oil spilling from a ruptured tanker spreads in a circle on the surface of the ocean. The radius of the spill increases at a rate of 9 m/min. How fast...
- Q The slope of the line through the distinct points (x1, y?) and (x2. y2) can be interpreted as the rate of change in_______with respect to______.
- Q A sports company has the following production function for a certain product, where p is the number of units produced with x units of labor and y units of capital.Complete...
- Q Consider the function defined by f(x) = Ax? 1Bx + 1Cx.a) Determine the end behaviour and the intercepts? [K, 2]b) Find the critical points and the points of...
- Q Consider the function f(x) = x^(2)e^(5x)For this function there are three important open intervals: ( - ?, A), (A, B), and (B,?) where A andB are the critical numbers.Find A______________...
- Q Consider the function f(x) = xe^(20x)f(x) has two inflection points at x = C and x = D with C<Dwhere C is ______________and D is _______________Finally for each of the...
- Q Find all solutions of the equation 2 sin x + ?3 = 0.The answer is A + B k? and C + D k ? where k is any integer,...
- Q Given ?ABC with ?B= 78,m?C = 52, and a = 16 inches, what is the length of b?O 31.343 inchesO 16.459 inchesO 19.861 inchesO 20.430 inches
- Q Determine the value(s) of x where the slope of the tangent line is horizontal. Use exact values.f(x) = 2x?(3x - 4x)
- Q Consider the function f(x) = 2x^3 + 6x^2 - 144x + 7,-6?x?5.This function has an absolute minimum value equal to _______and an absolute maximum value equal to ___________
- Q Given function g(x)= 8x^3 - 108x^2 + 480x, find the first derivative, g'(x)____________Notice that g'(x) = 0 when x = 4, that is, g'(4) = 0.Now, we want to know...
- Q Consider the graph of y = f(x), shown below.The maximum function value is___________and the minimum function value is__________The function is increasing on the interval__________and decreasing on the interval____________(Enter your answer(s)...
- Q Mark the critical points on the following graph.
- Q Consider the function f(x) = x? - 50x +11, 4 ? x ? 11. The absolute maximum of f(a) (on the given interval) is at and the absolute maximum of...
- Q Question 6Suppose sin?=3/5 , sin? =8/17. Moreover, suppose ? is in Quadrant II and ? is in Quadrant I.Find the following.sin(?+ ?)=_________cos(?+?) =_________
- Q Given f(x) = 2|x 7| +6Give a closed interval in the form [a,b] that the mean value theorem would:NOT APPLYWOULD APPLY
- Q Find the point on the tine y = 10x +1 closest to the point (4,3).(a) The function giving the distance between the point and the line is s =(b) The...
- Q Find a simplified expression for tan{sin?(t/7)}
- Q Let f(x) = x^3 + 3x^2 1.Calculate the derivativef'(x) = 3x^2 + 63Calculate the second derivativef''(x) = 6x + 6Note intervals are entered in the format (-00,5)U(7,00) (these are two...
- Q The function f(x)=9x + 2/x has one local minimum and one local maximum.This function has a local maximum at x=_______________with value___________and a local minimum at x =_____________with value________________
- Q Consider the function f(3) = 2x + 7x^-1 . For this function there are four important intervals:(-?, A], [A, B),(B,C], and [C,?) where A, and C are the critical numbers...
- Q Find the point on the tine - + 5y + 5 = 0 which is closest to the point (-2,-3).
- Q (1 + sec(t))(1 - cos(t))=Simplify further using identity sec(t)=1/cos(t)(1 + sec(t))(1 cos(t))=
- Q A stone is dropped into a calm lake causing a series of circular ripples. The radius of the outer one increases at 0.2 m/s. How rapidly is the disturbed area...
- Q Find the value of c on the interval (a, b)such that f'(c) =f(b)-f(a)/b - af(x) = 2x 3x + 180x +1 on interval [-8, -1]average rate of changeC =(enter answers...
- Q A large totem pole in the state of Washington is 100 feet tall. At a particular time of day, the totem pole casts a 249- foot-long shadow. Find the measure...
- Q Given the function g(x) = 4x 24x + 36x, find the first derivative, g'(c).Notice that g'(x) = 0 when I = 3, that is, g'(3) = 0.Now, we want to...
- Q Consider the function w() = - 12x? + 30x? - 2. Differentiate w and use the derivative to determine each of the following.All intervals on which w is increasing. If...
- Q Consider the function f(x) = 3x^2 - 2x + 8, 0 ? x ? 8.The absolute maximum of f(x) (on the given interval) is at x =and the absolute minimum...
- Q When a certain object is placed in an oven at 540C, its temperature T(t) rises according to the equation T(t) = 540(1- e^-0.1t), where t is the elapsed time (in...
- Q An airplane passes over a control tower at noon and continues to fly west at 100 km/h.A second airplane passes over the same tower at 1:00 p.m. flying south at...
- Q Consider the function r(a) = 36x?. + 270x? + 480x +20. Differentiater and use the derivative to determine each of the following.All intervals on which r is increasing. If there...
- Q What are the coordinates of the image of the point (-4, 9) after a 90 rotation followed by a translation 3 units to the left?
- Q Solve for x Rand to the nearest tenth if necessaryA right angle triangle with ?35, h = 16 and p = x.
- Q Consider the function f(x) = x?-50x +11The absolute maximum of /(w) (on the given interval) is atand the absolute maximum of /(m) (on the given interval) isThe absolute minimum of...
- Q Find the relative maximum and minimum values.f(x , y) = x + xy + y - 16y + 85Select the correct choice below and, if necessary, fill in the answer...
- Q IFind the relative maximum and minimum values.f(x,y) = e? + 8y + 9Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice.A. The...
- Q Find the relative maximum and minimum values.f(x, y) = e ^2x + 8y+ 9Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice.(A)....
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