Calculus question and answers for October 09, 2023
- Q For f(x)=?x and g(x) = 4x + 1, find the following composite functions and state the domain of each.(a) fog(b) gof(c) fof(d) gogOB. The domain of g of is all...
- Q Define(a) Show thatS(h)and state C1.? f (x+2h) +4f(x + h) ? 3f(x)=2hf'(x) - S(h) = c?h + c?h + c3h4+...
- Q Define(a) Show thatand state C?.S(h)-f(x+2h) +4f(x+h)-3f(x)2hf'(x) - S(h) = c?h + c?h + c3h + ...4
- Q [5 P] For the following differential equation, determine (without solving) an intervalon which the solution of the equation is certain to exist and be unique. Justify youranswer.(int)y + y =...
- Q Linearize the following ODE and find the corresponding initial conditions:x + 2x + sin x = 0.5,x (0) = -1, x(0) = 0
- Q Choose a suitable method, find the general solution of the following second order differential equations.a) dy/dx + 4y = 5sin(3x)b) 2(dy/dx) + 18y = 6tan(3x)Justify the reason for the chosen...
- Q Consider the differential equation dy/dx = 3(2x + 1)sin(x+x+?/2). (A) Find the equation of the line tangent to the solution curve at the point (0, 3).(B) Find the second derivative...
- Q What is the area of the region in the first quadrant enclosed by y=e^(-x^2/4) and the line y = 0.5.A) 0.516 sq unitsB) 0.240 sq unitsC) 0.480 sq unitsD) 1.032...
- Q Which of the following integrals correctly gives the area of the region consisting of all points above the x-axis and below the curve y= - x^2 + 2x + 8....
- Q Suppose the rate of growth of bacteria in a Petri dish is given by q(t) = 6?, where t is given in hours and g(t) is given in thousands of...
- Q For the following functions, f(x, y) = 4x^2 + 2y^2 8xy. Find the minimum using steepest descent method starting from initial point (2,3). Calculate optimum step size at every step.
- Q Find grad f(x) for each of the following functions:(a) f(x) = xo ' x (b) f(x) = |x|, x?0. (c) f(x) = (xo ' x)^2
- Q Solve the equation in the real number system: 2x + 3x + 2x + 3 = 0.
- Q Determine the domain of the function of two variables f(x ,y) = ?y + 9x.
- Q Determine the intervals on which n is continuous. Enter the solution using interval notation. n(x)=13x/8-xn is continuous on=____
- Q Solve the following second order differential equation and initial conditions for the timerange shown using the following method.y" + y = u(t-2), y(0) = 0 and y' (0) = 2,...
- Q Sketch the graph of y/6 - x/2 = 1. (Graph by selecting a type of graph, then select the center, then moving the cursor until the graph is correct).
- Q Find the length of the missing side. Leave your answer in simplest radical form.A right angle triangle with 11 cm, 4 cm.
- Q Given x = ?/3, what is the exact value of cos(2? - x)?a. 1/2b. -1/2c. ?3/2d. -?3/2
- Q Determine the zero(s) of p(x)= x + 13x + 42x.The zeros are x =
- Q Suppose an investment account is opened with an initial deposit of $12,000 earning 7.2% interest compounded continuously. How much will the account be worth after 30 years?How much less would...
- Q Graph and find the solutions for the quadratic function x- 4x + 4
- Q The total number of solution of the equation (x - 2) + {x 2} = 4 is equal to (where {:} is fractionalpart function)
- Q Sodium chlorate crystals are easy to grow in the shape of cubes by allowing a solution of water and sodium chlorate to evaporate slowly. If V is the volume of...
- Q Find the indicated derivatives of the following functions. No need to simplify.a. Find f'(x) where f(x) = arctan (1 + ?x)b. Find dy/dx where y is implicit defined by sin(2yx)...
- Q If t = sin 42", express csc 84 in terms of t:(A) 1/2t?1-t(B) 1/2t(C) 2t(D)?1-t(E) 2/t?1-t
- Q (10 pts) Compute the Fourier series for the function f(x) = on (-,). Then find a valuefor which the resulting sum is conditionally convergent, but not absolutely convergent. (Youust show...
- Q .Find a general solution toy" - 2y + 1y =12.5eltt + 1Use a and b for the constants of integration associated with the homogeneous solution.
- Q Find the solution tox' = yy' =12x +4yif (0) = 0 and y(0) = 8.
- Q A spherical balloon is being inflated. Find the rate (in ft2/ft) of increase of the surface area (S = 4?r) with respect to the radius r when r is each...
- Q Consider the transformation of the 4-vector (1,0) under a boost in the direction:(1,0)? (7?-?-1),where r= ?v-1 parameterises the boost.Writing r = cosh? show that the boost corresponds to the transformation...
- Q Note the following binomial expression.(3x + 3y)The expansion of this binomial has 4 terms. How many of the four terms shown below are correct:81x + 81xy + 81xy + 27y^4A)...
- Q A company makes computer chips from square wafers of silicon. A process engineer wants to keep the side length of a wafer very close to 18 mm and needs to...
- Q Without graphing the function y= 7 cos(-9x), determine its amplitude and period. Leave answers in exact form; type pi for ?.amplitude = ?period = ?
- Q Consider the following problem:maximize (minimize) 3x + y subject to the constraints: 4x-3y= 9 and x + z = 9(a) Write down the Lagrangian function.(b) What are the first-order conditions?(c)...
- Q Find the complete integral and singular integral of non-linear PDE :u(1+|Dul)=1Partial differential equation
- Q Solve the seperable differential equation:dy/dx = x/e?siny
- Q Solve the linear differential equation: y' + 3y = sin 2x
- Q Find the amount of money that results from 1000 dollars invested at 4 percent compounded quarterly after the period of 6 months.
- Q Suppose that p(x, y)-represents the production of a two-product firm. The company produces x units of the first product at a cost of c? each and y units of the...
- Q Does the equation specify a function with independent variable x? If so, find the domain of the function. If not, find a value of x to which there corresponds more...
- Q In a recent year, companies spent a total of $89.6 billion. on newspaper, television, and radio ads. The total amount spent on television and radio ads was only $3.2 billion...
- Q Given the function f(x)=3x (x-2)(x+4), find the following:a. The real zeros and the multiplicity of each (you may or may not need all blanks, just fill in what is needed).ZERO:______...
- Q Let's say we want to find the final grades for 3 girls, and we know what their averages are for tests, projects, homework, and quizzes.Student ...
- Q Determine p'(0). Enter DNE if the derivative fails to exist.Determine q'(0) Enter DNE if the derivative fails to exist.
- Q Use your calculator to evaluate cos?(-0.06) to at least 3 decimal places. Give the answer in radians.
- Q Solve the non homogeneous linear differential equations.y"'-3y" + 3y' - y = x - 4e^x
- Q Find an equation of the circle that has center (-6, 5) and passes through (-2,-2).
- Q A weather balloon is sent up to measure the air pressure, temperature, and dew point at a particular location. It radios back the following information: Time (s) Altitude (ft)...
- Q Determine the value(s) of the constant k for which the following system of equations hasa). no solutionsb). one solutionc). infinitely many solutionsx + y = 62x + 2y = k
- Q Evaluate the determinant of the matrix.-6 2-3 10The determinant is
- Q What is the discriminant of 6x2 - 2x - 3=0(a)76(b)68(c)29(d)none of these
- Q Solve each of the following initial value problems:(a) y'? = y?+ 2y?y? = 2y? - y? ends A and B are fixedy? (0) = 3, y?(0) = 1 babe three...
- Q Solve the system of differential equations: ...
- Q Find the value within [0, 2?) for function f(?) = 7 cos(7?) to reach its minimum value.?=
- Q Write a degree 3 Maclaurin Polynomial for f(x) = -4 sin(4x).
- Q Suppose a = 6 and b = 11.Find an exact value or give least two decimal places:sin(A) =cos(A) =tan(A) =
- Q Consider the differential equation:f'(x) = 3x + 11. Find the general solution for f(x).2. Find the solution for the differential equation with the initial condition f(0) = 2.3. Find the...
- Q Two sides and an angle are given. Determine whether the given information results in one triangle, two triangles, or no triangle at all. Solve any triangle(s) that results.B = 44,...
- Q A man has 6 shirts and 5 ties. How many different shirt and tie arrangements can he wear? He can wear _______ different shirt and tie arrangements.
- Q For the following functions, f(x,y) = 4x + 2y2 Bxy. Find the minimum using steepest descent method starting from initial point (2,3). Calculate optimum step size at every step.
- Q At a computer store, a customer is considering 7 different computers, 8 different monitors, 9 different printers and 3 different scanners. Assuming that each of the components is compatible with...
- Q If you make $2000 in Gross Income every month, but 35% is taken out in taxes, what will your monthly Net Income paycheck be? a) $1200b) $1675c) $1300
- Q Use the algorithm for Euler's method to determine approximations to the solution to the initial value problemy' = 3x(y + 2),0?x? 1,y(0) = 1 h = 0.2And compare these with...
- Q Find the singular points and then classify each one as a regular or irregular point.(x - 2x - 3)y" + x(x ? 2)y' - (x + 1)y=0
- Q Admission into an amusement park for 4 children and 2 adults is $116.90. For 6children and 3 adults, the admission is $175.35. Assuming a different price forchildren and adults, what...
- Q Find the dimensions of an open rectangular box of maximum volume and having an area of 48 ft that can be constructed from a piece of cardboard. (Let / represent...
- Q Sketch the region of integration and change the order of integration?? ??4-2_0 f(x,y) dydx
- Q Find equations of the tangent plane and the normal line to the given surface at the specified point.x+y+z= 8exyz, (0, 0, 8)(a) the tangent plane(b) the normal line(x(t), y(t), z(t))...
- Q The general solution of the differential equationdy dx + xsin2y = xcosy is(a) tan y=(x-1)+c.e(b) tan y=(x-2)+c.e-x(c) tan y=(x-1)+ ce-x(d) cot y =(x-1)+cex
- Q Evaluate the expression without using a calculator.arccos 1 2
- Q Traffic signs re regulated by the Manual on Uniform Traffic Control Devices (MUTCD). The perimeter of a rectangular traffic sign is 104 inches. Also, its length is 8 inches longer...
- Q Assume that f(-1)= -2. Assume also that the graph of y=f(x) is symmetric with respect to the line x=2. Find another value for the function.
- Q 4. The top eyeglass retailers last year were XrayVision, YesSpecs and ZoomGlasses. Together, they accounted for 69% of total market sales. The combined share of Xray Vision and YesSpecs was...
- Q The general solution of the differential equationxy' = y + ?x + y for x > 0is given by (with an arbitrary positive constant k)(A) ky = x + ?x...
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