Basic Math question and answers for August 10, 2023
- Q Use the ε-δ definition of limits to prove that lim x3 −2x2 −2x−3= −6. 3 markx→1Hint: This question needs students have a thorough understandingof the proof by the ε-δdefinition as...
- Q A manufacturer of men’s shirts determines that her costs willbe 500 dollars for overhead plus 9 dollars for each shirt made. Heraccountant has estimated that her selling price s(x)should be...
- Q Sketch the region bounded above the curve of y=(x^2) - 6, belowy = x, and above y = -x. Then express the region's area as oniterated double integrals and evaluate...
- Q Let r : R->R3 be a path with constant speed,satisfyingr\"(t) = (4 sin(2t))i + (-4 cos t)j + (4 cos(2t))k for all tbelongs to R:Find the curvature w.r.t. t of...
- Q Greg wants to build a rectangular enclosure for his animals. Oneside of the pen will be against the barn, so he needs no fence onthat side. The other three sides...
- Q Find the equation of the tangent line to the circle(x+2)2 +y+5)2 =4 at point (-4,-5) (
- Q Brain weight B as a function of body weight Win fish has been modeled by the power function B =0.007W2/3, where B and W aremeasured in grams. A model for...
- Q Use cylindrical shells to find the volume of the solid generatedby rotating the given region about the x-axis.y=e^x, y=1, x=2
- Q Use Lagrange multipliers to show that the shortest distance fromthe point (x0,y0,z0)to the plane ax+by+cz=dIs it the perpendicular distance?(Remind yourself of the equation of the line perpendicular to the plane.)How...
- Q Find the radius and interval of convergence of the series X∞ n=13^n (x − 5)^n/(n + 1)2^n
- Q Determine the location of the center of mass of the regionbounded above x^2 + y^2 = 100 and below y = 6. Assume the regionhas a uniformdensity.Two answer I got...
- Q Evaluate the integral. (Use C for the constant ofintegration.)√(-x^2-6x+27)
- Q 1. Find the critical numbers for the following functions(a) f(x) = 2x 3 − 6x(b) f(x) = − cos(x) − 1 2 x, [0, 2π]2. Use the first derivative test...
- Q Consider the functionf(x) = x 4 − 4x 2 . Determine the following:• The (x,y) coordinate pairs of the local minima and localmaxima.• The (x,y) coordinate pair of the absolute...
- Q Find the maximum volume of a rectangular box that can beinscribed in the ellipsoid ?^2/81+?^2/36+?^2/36=1 with sidesparallel to the coordinate axes. Volume =
- Q Find the maximum volume of a rectangular box that can beinscribed in the ellipsoid ?^2/81+?^2/36+?^2/36=1 with sidesparallel to the coordinate axes. Volume =
- Q 7. Find the maximum and minimum of the function. f (x, y) = x^ 2+ y^ 2 − xy − 3x − 3y on the triangle D ={(x, y)| x...
- Q The length, width, and height of a box are measured as 5 ft,4 ft, and 8 ft, respectively, with an error in measurement of atmost 0.3 ft in each. Use differentials to estimate the...
- Q A rectangular storage container with an open top is to have avolume of 10 m3. The length of this base is twice thewidth. Material for the base costs $10 per...
- Q Consider the equation f(x,y) = −4x2+4x+y2+2y, the picture showssome of it’s level curves.a. Completing the square, write the equations and identify thetraces f(x,y) = k for k = −1,0..(b) Draw...
- Q A machine that costs $5000 is to be replaced in 5 years by a newone. The old machine at that time would be worth $500. How muchshould the periodic payments...
- Q A positive number is added to the reciprocal of its square root.Use Calculus methods to answer the following questions:what ifanything, is the smallest such sum? What, if any, positive x-valueswill...
- Q 1.List 10 facts about exponential functions.2. List 10 facts about logarithm functions.
- Q CalculusThe marketing department for a cell phone telephone company hasdetermined that the demand for their phone obeys the followingrelationship: p= -0.02+200 , (0 ≤ p ≤10,000) , where p denotes...
- Q Solve the initial value problem z(5)+2z'''- 8z' = 0, where z(0) = 4, z'(0) = 2,z\"(0) = 8, z\"'(0) = 12, and z(4)(0) = 8
- Q Compute the hydrostatic force on a circular plate of radius 5meters suspended vertically in water so that the top of the plateis at the surface of the water. (The density...
- Q Suppose that f is a differentiable function with derivative f\"(x) = (x − 3)(x + 1)(x + 5). Determine the intervals of x for whichthe function of f is increasing...
- Q y'' + y = teitInclude the starting particular solution with unknown functionsof t: A and B. Identify the system of equations to solve to find A'and B'. Write the integrals...
- Q What are the aspects and impacts of Air ConditioningRecharging?
- Q Questionnnnnnna. Let V and W be vector spaces and T : V → W a lineartransformation. If {T(v1), . . . T(vn)} is linearly independent inW, show that {v1, ....
- Q Use the Gauss-Jordan elimination method to solve the followingsystem of linear equations. State clearly whether the system has aunique solution, infinitely many solutions, or no solutions. { ? +2? =...
- Q Follow the steps bellow to construct a general solution to theequation:y'' + y = 3sect -t2+1a. find the general solution to the homogeneous version of theproblemb. find the particular solution...
- Q Can you apply L'Hopital's rules to the following limit?lim x approaches infinity (1+cos(x)) / sin(x)true or false
- Q Find the sum (n=5, to infinity) of the series (n2-n)/2n
- Q 1.Find the critical numbers of the function f (x) = x^3− 12x in theinterval [0, 3]. Then find the absolute maximum and the absoluteminimum of f(x) on the interval [0,3].2....
- Q Part A: Express the quadratic function in standard form (vertexform). ?(?) = 1 − 12? − 4? 2Part B: Find the quotient and remainder using syntheticdivision. ?^4 + 2?^3 −...
- Q h(t)=60t-t^4+1 represents the height of an object with respectto time.what is the height of this object after t=5 sec?find derivative using limits definition?what is the velocity of the object at...
- Q Suppose that a1-12 and an+1 is a third ofthe value of an for all n=1,2,3,4,5.... naturalnumbers.a) find the first foudn terms fo the sequenceb) find the formula for all values...
- Q Solve using Implicit Differentiation showing all steps:a.) xy^2-y^2=6b.) x^2 − 2xcosy + y^2 = 3c.) x = x + y/2y − xd.) x^2 + 4cos(xy) − y^2 = 8Thank you!
- Q Consider the function. f(x) = x^2 − 1, x ≥ 1(a) Find the inverse function of f.f ^−1(x) =(b) Graph f and f ^−1 on the same set of coordinate axes.(c) Describe...
- Q aparticle moves aling a straight line and its position at time t isgiven by s(t)= (t^3)-13.5t^2+54t where s is measured in feet and tis seconds. consider t in the interval...
- Q Use Newton's method to approximate the indicated root of theequation correct to six decimal places.The root of x4 − 2x3 + 4x2 − 8= 0 in the interval [1, 2]x...
- Q Question 1f is a function whose domain is (0,∞) and whose firstderivative is f ' (x) = (4 − x)x -3 for x >0a) Find the critical number(s) of f....
- Q Suppose f is a twice differentiable function such thatf′(x)>0 and f′′(x)<0 everywhere, and consider the followingdata table.x     0      1      2f(x)  3      A      BFor each part below, determine whether the given values of A...
- Q Please give a brief description about the Remote data like REST,JSON, XML, AJAX and SOAP API’s ?
- Q You are given that cos(A)=-7/25, with A in Quadrant lll andcos(B)=3/5, with B in Quadrant l. Find cos(A+B). Give your answeras a fraction.
- Q The planex + y + 2z = 12intersects the paraboloidz = x2 + y2in an ellipse. Find the points on the ellipse that are nearestto and farthest from the origin.nearest...
- Q 1. You are given the function f(x) = 3x^4 + 4x^3a) Find the x and y- intercepts.b) Find the critical number(s) of f.c) Find the interval(s) of increase and decrease...
- Q Boyle's Law states that when a sample of gas iscompressed at a constant temperature, the pressure P and volume Vsatisfy the equation PV = C, where C is a constant....
- Q Create your own scenario in which you can compare the cost fortwo choices for the same service.You will need to create two equations, each of which shouldinclude::1. fixed cost2. variable...
- Q In an RL series circuit with L = 1/100 H, R = 20 Ω, and E = 60V. Determine the limit of the maximum current reached (At thefunction you found...
- Q A store sells about 360 calculators peryear. It would cost thestore $8 to store one calculator for the whole year. On the otherhand, it costs $10 each time the store...
- Q 1. A 20 foot ladder leans against a vertical wall. The bottom ofthe ladder slides away from the wall at 2 ft/sec.a. How fast is the top of the ladder...
- Q Using the pair of compasses and ruler only, constructTriangle GBC with angle CBG = 30*, /BC/ = 9.5cm and /BG/=12cmL1, the locus of points 6cm from CL2, the perpendicular from...
- Q Find the area of the surface obtained by rotating the circlex^2+y^2=49 about the line y=7. (Keep two decimal places)
- Q Find the absolute maximum and minimum values of the functionf(x, y) = x^2 + ((4/3) y^3) − 1 on the disk x^2 + y^2 ≤ 1.
- Q A company calculates the following for an item that they produceand sell. The revenue, R(x), from the sale of 90 items is 2300dollars. The marginal revenue when 90 items are...
- Q Find the volume of the solid that lies within the spherex2+y2+z2=64, above the xy plane, and outside the conez=7sqrt(x2+y2)
- Q Determine whether the curve denoted by the vector function r(t)= <2 + sin(5t), -6, 3/2 (cos(5t))> lies on the surface 9x^2 -36x - y^2 + 4z^2 = -36.
- Q P1.Write the Taylor series for f(x) = cosx about x = 0.State the Taylor polynomials T2(x),T4(x), and T6(x) (note thatT3(x)will be the same as T2(x), andT5(x) will be the same...
- Q If the producer of a commodity spends x thousand dollars onadvertising, then Q(x)=43-10e^(-1/2x) thousand units of thecommodity will be sold.(a) How many units will be sold if no money is...
- Q Use Newton’s method to find x1, x2 and x3 with the given x02/x− x^2 + 1 = 0 x0 = 2
- Q Evaluate the iterated integral.integral sqrt(pi) to 0 integral 3x to 0 integral xz to 0 of15x^2 sin(y) dydzdx
- Q An underground tank is a hemisphere with radius 4 feet (i.e. itis half a sphere, and so horizontal cross-sections are circles ofvarying radius). It is filled to the top with...
- Q limx-->0+(4x+1)cotx=could you please show work and explain which rules you used.Thank you
- Q (a). Let S be the surface defined by x^4 − 3x^2y^2 + 4z^2 = 17.Find the equation of the tangent plane to the surface S at (1, 0,2).(b)Let f(x,y) =...
- Q A travel agency is planning a trip to England for 100members of a college faculty. The plane fare will be $600 perfaculty member if all members attend the trip. With...
- Q given the function y=x+cosx on the interval [0,2pi] find theintervals of increasing and decreasing, local or absoluteextrema(s), the intervals of concavity and the inflection points.use the information to sketch the...
- Q A rectangle is to be inscribed in the ellipse (xb)^2+y^2=1,where b>0 is an unknown real number.What should the dimensions of the rectangle be (in terms of b)to maximize its area?...
- Q create a power series for 5/2x-3 c=-3create a power series for 5/(2x-3)^2 c=-3
- Q By justifying your answer determine whether the function T is alinear transformation.T:P3→ P4defined as T(a+bx+cx2+dx3)=b−ax+adx4T:P3→ M2,2 defined asT(a+bx+cx2+dx3)= [−d,c,√3a,a+b] its a matrix
- Q In each case, compute the derivative dy dx . Do not simplifyyour answer.a) y= 4x^3e^5xb) y=ln {(x^3 + 3x)(2x^4 -1)} using product rulec) f (x) = x^4 ln 3x -...
- Q What is the radius of convergence for (( 2x-3)^n) / (n+4)^2 *5^n+1
- Q part A)The antiderivative of an acceleration function is aposition function.A)TrueB)FalsePart B)A right Riemann sum always gives an underestimate.A) TrueB) FalsePart C)Integration by substitution is the process that reversesthe chain rule.A)...
- Q Find the point on the curve y=4x+4 closest to the point(0,8)(x,y)=
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