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    Calculus and Analysis

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    Vectors, Gradients and Rate of Change

    8. The Intergalactic Ship Zora is hanging motionless at (5, 1, 10) (Universal Galatic Coordinates) when the crew spots an interesting object at (7, 5, 6). The temperature in that part of the galaxy is given by T(x,y,z) = x2 + y/x + z3. As the crew starts to move the Zora directly toward the unknown object, what is the rate of ch

    Center of Mass of a 4D Pyramid

    Find the center of mass of a 4-D pyramid (cube base) using algebraic means (no calculus is allowed). I need a step-by-step solution with all work shown.

    Center of Mass of 4D Pyramid

    Find the center of mass of a 4D pyramid (cube base) using calculus (25 credits if you can solve it with only algebra).

    Limits and Piecewise Functions

    Please help with the following problems regarding limits and piecewise functions. 1) Let f(x) {o if x is a natural odd number {1 otherwise Does f(x) have a limit as x approaches infinity? Explain you answer. 2) Let f(x) {1 if x is a natural odd number { 1-1/x

    Limits and Continuity Domains

    What is the domain of the function f(x) = square root of x-1/square root of x2? Is this function continuous everywhere where it is defined? Explain.

    Limits and Continuity Graph Functions

    Sketch by hand the graph of a function f that satisfies (a) f(2)=3 and (B) lim as x approaches 2 of f(x)=4. Is the function f(x) continuous at x=2? explain.

    Secant Lines

    Let f(x) = cos(x). Let p=(pi,-1) be a point on the graph y = f(x). a) calculate the slope of the secant line passing through P and F(pi+0.2), (pi+0.2)) b) calculate the slope of the secant passing through P and (pi-0.1),f(Pi-0.1)) what would your guess on the value of slopes of secant lines passing through P and other p

    Differential Equations: LRE and CRE Circuits

    A 20 ohm resistor, a .05 farad capacitor, and an alternating power source equal to 40 cos(t) are placed in series. If the initial charge on the capacitor is 3 coulombs, find a general formula for the charge at any time t.

    Differential Equations: Electromotive Force and Maximum Current

    An electromotive force of 100 volts is in series with a 2 henry inductor and a 50m ohm resistor. a. Determine the current i at any time t after the switch is closed b. Determine the maximum current that can be obtained in the simple circuit described. Please see the attached file for the fully formatted problems.

    Differential Equations and Rate of Change

    A tank initially contains 100 gallons of a solution that holds 10 pounds of a chemical. A solution containing 1 pound of the chemical runs into the tank at a rate of 4 gallons per minute, and the well-mixed mixture runs out of the tank at a rate of 6 gallons per minute. a. How much chemical is in the tank after 25 minutes? b

    Differential Equations and Rate of Change: Example Problems

    A tank contains 54 gallons of pure water. A salt water solution with 2 pounds of salt per gallong enters the tank at a rate of 3 gallons per minute, and the well-stirred mixture leaves the tank at the same rate (3 gallons per minute). a. How much salt is in the tank at any time t? b. When, to the nearest minute, will the wat

    Applying Differential Equations and Logistic Equations

    The number of bacteria in a Petri dish was initially determined to be 200. After one hour, the number had increased to 500 and after another hour to 1,000. Assume that the rate of bacterial growth in the dish at any time t can be calculated using the logistic equation dB/dt = B(a-bB), which I know to use the formula B = aBo/(bBo

    Nonlinear Differential Equations: Chemical Reactions Problem

    Question: A Chemical X is produced from a reaction involving chemicals A and B. The rate of production of X varies directly as the product of the instantaneous amounts of A and B present. The formation of X requires 6 pounds of A for every 4 pounds of B. 30 pounds of A and 20 pounds of B are present initially and 10 pounds of

    Differential Equations : Phase Lines and Bifurcation Diagrams

    Please see the attached file for the fully formatted problems. 22. (a) Use PhaseLines to investigate the bifurcation diagram for the differential equation .... where a is a parameter. Describe the different types of phase lines that occur. (b) What are the bifurcation values for the one-parameter family in part (a)? (c) U

    Conical funnel

    Water is running out of a conical funnel at the rate of 3 cubic inches per second. The funnel has a radius of 2 inches and a height of 8 inches. How fast is the water level dropping when it is at a height of 5 inches? Round your answer to the nearest tenth.

    Inverse of a function

    Let f(x)=3+x^2+tan(pie*x/2), where -1<x<1. a. find f-1(inverse) of (3) b. find f(f-1(5))

    Partila Differential Equations : Ito's Lemma

    Please see the attached file for the fully formatted problems. Suppose that S satisfies: dS = a(S,t)dt + b(S,t)dX Show that for any functions g1(S,t) and g2(S,t), the following is true: (Note: I don't know if Itô's lemma is used in the proof or if you can use some Calculus identity or rule to determine the proof.

    Calculus: Finding Limits

    Please choose the correct answer: 1. Let f(x) = 2x^2 + 11x + 15 and g(x) = 2x^2 + 9x + 9. Then lim f(x)/g(x) = x=>-3 5/3 4/3 1 2/3 7/9 4/9 5/7 4/7 3/4 9/4 9/10 none of these

    Limiting value of a function.

    Please choose the correct answers (Indicate final answer) 8. lim (2x^3 - 7x^2 + 3x - 4)/(3x^3 + 5x - 6) = x=>oo 2/3 3/2 0 1 -1 oo none of these

    Acceleration Rate of Change of Homer Simpson

    Homer Simpson lies directly in the path of the flame-spewing juggernaut, with only the meager acceleration of the family station wagon standing between him and utter destruction. Assume Homer's velocity (in feet per second) is given by the equation: V(t)=t^3-4t^2-t-x+1 , where t is measured in seconds and . Answer the f

    17 Calculus Problems

    See attached file for full problem description. 1. Use the definition of the derivative to find f(x) given f(x) = square root (x). 2. A ball thrown vertically upward at time t = 0 (s) with initial velocity 80 ft/s and with initial height 96 ft has height function: y(t) = -16t^2 + 80t + 96. a) What is the maximum hei