Basic Math question and answers for July 12, 2023
- Q a) Find the Taylor series for sinh(x) (centered at x=0), for e^x(centered at x=0) and hyperbolic sine and hyperbolic cosine.b) same as a but cosh(x) instead
- Q Given v?(t)=2ti+j, find the arc length of the curve v(t) on theinterval [?2,3]. You may use technology to approximate yoursolution to three decimal places.
- Q Question 1: Show that x = h + r cos t and y = k + r sin trepresents the equation of a circle.Question 4: Find the area above the...
- Q Solve the following initial value problem. y?? ? 10y? + 24y ?=?5x + e^(4x), y(0) ?=? 0, y?(0) ?=? 4(not using Laplace)
- Q The function needs to have at least one maximum or minimumvalue. A. Create a function thatrequires quotient rule (with a variable in the denominator). Thefunction needs to have at least...
- Q Find T(t), N(t), aT, and aN at the given time t for the spacecurve r(t). [Hint: Find a(t), T(t), aT, and aN. Solve for N in theequation a(t)=aTT+aNN. (If an...
- Q la place transform of1. y´´+4y´+6y_=0, y(0)=1, y´(0)=-42. y´+y=t^2 , y(0)=0
- Q second order linear non-homogeneoussolve the following equationsd2y/dx2+y=5ex-4x2
- Q What is the absolute max / min value for the function f(x) = xsqrt 1 - x on the interval [ 1 , 1 ]
- Q Aprojectile is launched at an angle of 60 degrees to the horizontalfrom 6.5ft above the ground at an initial speed of 100 ft/sec.Assume the x-axis is horizontal, the positive y...
- Q (6) Consider the function f(x, y) = 9 ? x^2 ? y^2 restricted tothe domain x^2/9 + y^2 ? 1. This function has a single criticalpoint at (0, 0)(a) Using...
- Q A company manufactures two types of electric hedge trimmers, oneof which is cordless. The cord-type trimmer requires 2 hours tomake, and the cordless model requires 4 hours. The company has...
- Q Set up (Do Not Evaluate) a triple integral thatyields the volume of the solid that is below the spherex^2+y^2+z^2=8and above the conez^2=1/3(x^2+y^2)Rectangular coordinates b) Cylindricalcoordinates c) Sphericalcoordinates
- Q Prove the transitive property of similarity: if A~B and B~C,then A~C.
- Q a.)Using disks or washers, find the volume of the solid obtainedby rotating the region bounded by the curves y^2=x and x = 2y aboutthe y-axisb.) Find the volume of the...
- Q Use the position function ?(?) = ?16?^ 2 + ?0? + ?0 for thefollowing vertical motion of objects on earth.5) An object is launched vertically from a 75ft building with...
- Q 1. Write an equation of the line perpendicular to the line y=-1/2x + 5 at (-4,3) and sketch its graph.Draw the graph of y= 3 sin 2x from x=0 to...
- Q 1] Find an? nth-degree polynomial function with realcoefficients satisfying the given conditions. If you are using agraphing? utility, use it to graph the function and verify the realzeros and the...
- Q describe the purpose of finding the first and second derivatives tosketch a graph of functions
- Q A chemist needs 10 liters of a 25%acid solution. The solution is to be mixed from three solutionswhose concentrations are 10%, 20% and 50%. How many liters of eachsolution will...
- Q Use Euler's method with each of the following step sizes toestimate the value of y(0.8), where y is thesolution of the initial-value problem: y' = y,y(0) = 5.(i) h = 0.8y(0.8)...
- Q Onthe moon the acceleration due to gravity is -1.6 m/s. a stone isdropped from a cliff on the moon and his the surface of the moon 40seconds later.How do i...
- Q Using a scalar surface integral, compute the surface area of theportion of the unitsphere that is above the cone z = sqrt(x^2+y^2)
- Q The exponent rules are needed in order to perform operations onpolynomials. In your own words:Explain what a polynomial is and identify the different parts of apolynomialExplain the different labels used...
- Q 1. solve the initial value problem.(t^(2)+1)y'+2ty=tant , y(0)=22.find the solution to this initial value problem.yy'=e^x+x , y(0)=y_0y_0 is a nonzero constant.
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