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Calculus and Analysis

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

Minimization of a triangle area

Find the altitude to the base of an isoceles triangle with a side length of 4, such that the area of the triangle is maximal.

Oscillating Inflow Concentration

Make a conjecture, on the basis of physical reasoning, as to whether you expect the amount of salt in the tank to reach a constant equilibrium value as time increases. In other words, will lim(t) -> infinite Q(t) exist? (see attachment for full question)

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

Distance travelled around box problem

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

Geometric series?

Determine if the following series converges and if possible give its sum 2/3 + 2/9 + 2/27 + 2/81 + ...

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

Graphs : Rectangular and Parametric Forms

Graph x=(t^2+2t+1)^(1/2) y=(t^3+2t^4)/t^2 a. Graph on the interval [0,3] b. Convert to rectangular form. c. Adjust the domain of the rectangular form to agree the parametric form.

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

Parametric Equations : Circle and Ellipse

Create parametric equations for: a. A circle of radius 2 centered at (3,1). b. An elipse with a horizontal major axis of length 5 and a verticle minor axis of length 4.

Maximum and Minimum Distance Word Problem

Johnny Steamboat wants to sail from his island home to town in order to purchase a book of carpet samples. His home island is 7 miles from the nearest point on the shore. The town is 35 miles downshore and one mile inland. If he can run his steamboat at 12 mph and catch a cab as soon as he reaches the coast that will drive 60


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