Explore BrainMass

Explore BrainMass

    Calculus and Analysis

    BrainMass Solutions Available for Instant Download

    Graphing Functions Inflection Points

    The function is f(x) = 5x^2 / (x^2 + 2) I need to find the x and y intercepts all asymptotes and inflection points. I know only how to do this if I have a closed interval if you could walk me through this step by step use the critical number and f'(x) and f''(x) graph

    Propagated error

    Find the propagated error for the area is the question: You must use differential to solve I cannot find the derivative of area of a triangle area = .5 b x h the base = 36cm height = 50cm and possible error for each is .25 cm

    Finding sets and functions

    (See attached file for full problem description with equations) --- Let . (a) Find the set of points at which . (b) Let . Find a set V such that f takes U onto V in a one-to- one fashion and the inverse function g on V. ---

    Temperature Change Differential Equations

    A solid metal sphere at room temperature of 20 degrees Celsius is dropped into a container of boiling water (100 degrees Celsius). If the temperature of the sphere increases 2 degrees Celsius in 2 seconds, what will the temperature be at time t=6 seconds? how long will it take for the temperature of the sphere to reach 90 degree

    Solving Calculus Problem

    File is attached. I need only the answers with work shown in very shortly. Please check my answers.

    Differential equations of Circles

    Differential Equation (XV) Formation of Differential Equations by Elimination Find the differential equations of all circles of radius (whatever their radii or positions in the plane xOy).

    Differential equations of all parabolas

    Differential Equation (XII) Formation of Differential Equations by Elimination Find the differential equations of all parabolas whose axes are parallel to the axis of y.

    Differential Equations of Exponential Functions

    Differential Equation (IX): Formation of Differential Equations by Elimination Eliminate the arbitrary constants from the equation: y = Ae^x + Be^2x + Ce^3x. Make sure to show all of the steps which are involved.

    Equations of Tangent Lines and Intercepts in Terms of a Variable

    Let f(x) = a(7-x^2) where a is not equal 0 (a) find, in terms of a, the equation of the line tangent to the curve at x = -1 (use point slope) (b) find, in terms of a, the y intercept of the tangent line at x = -1 (c) find the x intercept of the tangent line at x=-1

    Solutions, Electric Circuit and Step Function

    Find the general solution of each of the differential equation y ''- y ' = x2 . If the solution is not valid over the entire real axis, describe an interval over which it is valid. If k is a nonzero constant, prove that the equation y ''+ k2y = R(x) has a particular solution 1 y given by ..... Find the general solution of

    Solve the differential equation

    The presence of toxins in a certain medium destroys a strain of bacteria at a rate jointly proportional to the number of bacteria present and to the amount of toxin. If there were no toxins present, the bacteria would grow at a rate proportional to the amount present. Let x denote the number of living bacteria present at time t.

    position of the point is the sum of the distance

    For what position of the point (x, y) is the sum of the distance from (x, y) to the x-axis and twice the distance from (x, y) to the point (0, 1) a minimum? From Advanced Calculus, Taylor & Mann(1972), p.144

    Use of L'Hopital's rule

    Please explain how to evaluate the limit lim/k arrow to 0 f(x = h) - f(x)/h using the rules for finding the derivative of f.

    Differential Equation - Initial Value Problem

    11. Consider an electric circuit like that in Example 5 of Section 8.6. Assume the electromotive force is an alternating current generator which produces a voltage V(t) = E sinwt , where E and w are positive constants (w is the Greek letter omega). EXAMPLE 5. Electric Circuits. Figure 8.2(a), page 318, shows an electric circu

    Population Dynamics

    I think the solution is probably a simple modification to the predation equations: dN/dt = rN - cNP is the growth rate for the prey population and dP/dt = -dp + gcNP is the growth rate for predator population, where: N= prey density P = predator density d= death rate g = conversion efficiency of prey to predators r = p

    Rate of change of area

    For time t between 2 and 3 hours the radius of circle c is 5t-t^2-6 feet. at time t=2.6 hours the area of the circle is changing at a rate of ------. at time 2.6 hours the area of the circle is-----. a(t) = pie(5t-t^2-6)squared

    Differential Equations : Three Initial-Value Problems

    Theorem 8.3. Assume P and Q are continuous on an open interval I. Choose any point a in I and let b be any real number. Then there is one and only one function y = f(x) which satisfies the initial value problem y' + P(x)y = Q(x), with f(a) = b on the interval I. This function is given by the formula f (x) = be- A( x) + e-A( x

    Modeling Data for Linear Functions and Maximizing Profit

    1960 88 1970 121 1980 152 1990 205 1997 217 a) Model the data with two linear function. Let the independendt variable represent the number of years after 1960. b) With each function found in part a), predict the amount of maunicipal solid waste in 2005. c) Which of the two models

    Sand falls from an overhead hopper to form a right circular cone. If the cone formed has an angle theta find the rate of change of volume with respect to height? If the height is changing at 2cms per minute, what volume of sand is falling from the hopper when the height of the cone is 3 meters? (The volume of a cone is (1/3)pir2h where h is the height and r is the radius.)

    Sand falls from an overhead hopper to form a right circular cone. If the cone formed has an angle theta find the rate of change of volume with respect to height? If the height is changing at 2cms per minute, what volume of sand is falling from the hopper when the height of the cone is 3 meters? (The volume of a cone is (1/3)pir2

    Problem on Distance Formula

    To get to work Sam jogs 3 Kilometers to the train, then rides the remaining 5 kilometers. If the train goes 14 kilometers per hour faster than Sam's constant rate of jogging and the entire trip takes 45 minutes, how fast does Sam jog?