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Calculus and Analysis

Simulation : Skydiver in Free-fall

A skydiver, weighing 70kg, jumps from an aeroplane at an altitude of 700 metres and falls for (T) seconds before pulling the rip cord of his parachute. A landing is said to gentle if the velocity on impact is no more than the impact velocity of an object dropped from a height of 6 metres. The distance that the skydiver falls d

Setting up a Riemann Sum

I can't figure out exactly how to formulate a riemann sum. For example, when given y=x+2; [0,1], and told to "find the area of the region under the curve y=f(x) over the interval [a,b]. To do this, divide [a,b] into n equal subintervals, caluculate the area of the cooresponding circumscribed polygon, and then let n go to infin

Calculus : Reimann Sum and Limits and Continuity

34) The function f is continuous on the closed interval [1,5] and has values that are given in the table below. If 2 subintervals of equal length are used, what is the midpoint Reimann sum approximation of integral with 5 on top and 1 on bottom f(x)dx? Please given step by step explaination and answer is 32. x 1 2 3

Calculus : Antiderivative and Rate of Change

36)If the functions f and g are defines for all real numbers and f is an antiderivative of g, which statements are not true? I If g(x)>0 for all x, then f is increasing. II If g(z)=0 then f(x) has a horizontal tangent at x+a. III If f(x)=0 for all x, then g(x)=0 for all x. IV If g(x)=0 for all x, then f(x)=0 for all x.

Calculus : Differentiability and Maximizing Area

24) Let f be a differentibale function defined on the closed interval [a,b] and let c be a point in the open interval (a,b) such that. I f'(c)=0 II f'(x)>0 when a<or equal to x<c, and III f'(x)<0 when c<b<or equal to b. Which is true? Then tell why others false. a. F'(c)=0 b. F"(c)=0 c. F(c) is an abs. ma

Velocity, Continuity, Limits, Differentiability & Integrability

26) The vertical height in feet of a ball thrown upward from a cliff is given by s(t)=-16t^2+64t+200, where t is measured in seconds. What is the height of the ball, in feet, when its velocity is zero? 27) If the function f is continuous for all real numbers and the limit as h approaches 0 of f(a+h)-f(a)/h = 7 then which sta

Critical Points and Maximum and Minimum Values

Please see the attached file for the fully formatted problem. Find the critical points and use your test of choice to give local maximum and minimum values. Give those values. f(x) = x^2 /sqrt(x^2 + 4)

Find dy

Please see the attached file.

Differential Equations : Free Fall and Terminal Velocity

An object in free fall in a gravitational field is governed by the ODE m*dv/dt=mg + Fs, where m is the mass of the object, g=9.8 meters/sec is the acceleration of gravity, v(t) is the velocity of the object t seconds after it is released, and Fs denotes external forces acting on the object. In all that follows, assume that v(0)

Chaos : Conjugacy in Discrete Dynamical Systems

I am taking a course in Dynamics/Chaos and I am trying to prove conjugacy between the logistic and quadratic functions. I have some ideas, but cannot get the proof to work. Attached is a word document with the functions and problem.

Tangent through a point

A portion of a river has the shape of the equation y=1-x^2/4, where distances are measured in tens of kilometres, and the positive y-axis represents due north. the town of Coopers Crossing is situated on the river at its most northerly point. The town of Black Stump is 10 kilometres due south of Coopers Crossing. the town of And

Line Equations : Tangents & Normals

I) Find the equation of the tangent to y=x(1-x) at x=1 ii) Find the equation of the normal to y=x(1-x) at x=1 iii) Find the equations of the tangents to y=x(1-x) that pass through (-1, 1/4)

Differential Equation

Most drugs are eliminated from the body according to a strict exponential decay law. Here are two problems that illustrate the process. 1. The drug Valium has a half-life in the blood of 36 hours. Assume that a 50-milligram dose of Valium is taken at time t=0. Let m(t) be the amount of drug in the blood in milligrams t hours


Please see attachment. Require problems solving, also explanations etc for better understanding.

Calculus 3 and 4

Show all work. Please DON'T submit answers back to me as an attachment. Thank you. Determine whether the function is homogenous. If it is, state the degree: f(x, y)=5x^2 + 2xy

Oscillating Inflow Concentration

Oscillating Inflow Concentration A tank initially contains 10 lb of salt dissolved in 200 gallons of water. Assume that a salt solution flows into the tank at a rate of 3 gal/min and the well-stirred mixture flows out at the same rate. Assume that the inflow concentration oscillates I n time, however, and is given by ci(t

Functions : Tangent, Increasing or Decreasing and Area under a Curve

2. Let f be a function defined on the closed interval -3&#8804;x&#8804;4 with f(0) = 3. The graph of f', the derivative of f, consists of one line segment and a semicircle. a) On what intervals, if any, is f increasing? Justify your answer. b) Find the x-coordinate of each point of inflection of the graph of f on t

Minimization, maximization (Calculus)

An ant is walking around the outside of the cube in "straight" paths (where we define a straight path in this case as one formed by the edges of a cross section created by a plane slicing through the cube). For example, to get from point Q to point R in the picture above on the right, the ant walks along the red path. There are

Comparing Graphs : First and Second Derivatives

X -1.5 -1.0 -0.5 0 0.5 1.0 1.5 f(x) -1 -4 -6 -7 -6 1.0 -7 f'(x) -7 -5 -3 0 3 5 7 Let f be a function that is differentiable for all real numbers. The table above gives the values of f and its derivative f' for selected points x in the closed interv

Proportionality and Rate of Change Word Problem

A container has the shape of an open right circular cone. The height of the container is 10cm and the diameter of the opening is 10cm. Water in the container is evaporating so that its depth h is changing at the constant rate of -3/10 cm/hr. Show that the rate of change of the volume of water in the container due to evaporati


Let X(n)=Sum{1/(n+i), i=1->n}, find the limit of X(n) as n tends to infinity

Lower Estimate, Upper Estimate?

Please see the attached file for the fully formatted problems. 14) A power plant generates electricity by burning oil. Pollutants produced as a result of the burning process are removed by scrubbers in the smokestacks, Over time, the scrubbers become less efficient and eventually they must be replaced when the amount of pol

Solving Equations : Newton's Method

Please see the attached file for the fully formatted problem. The equation x2 - 3x + 1 = 0 has a solution for x>= 0. Give the third approximationby using Newton's method. Your first approximation is to be 1.

8 calculus problems

Please answer eight (8) calculus problems. Please show as much works as possible for every problem. The problems are posted in the following website:

Limits of Functions

For which real values alpha does lim {x -> 0+} x^alpha sin(1/x) exist? It is easy to show using the epsilon - delta definition below that this limit exists for all real alpha >= 1. In fact the limit is zero in this case. The case alpha equals zero is also quite simple and the limit does not exist. Consider the two sequence

Projectile motion

With this problem im seeking a detailed explanation. I already have some of the answers however i dont see how they were obtained. Can you please solve this and show me how each answer was obtained. My numbers are way off from what they should be. Thanks The quarterback of a football team releases a pass at a heigh