Use one-sided limits to find the limit or determine that the limit does not exist: limx => 4 16-x^2 / 24-x The problem might be easier to read like this: limit 16 - x^2 x --> 4 24 - x
Find a Cartesian equation for the curve described by the given polar equation. r= 5/(3-4sin theta)
3. Use calculus to sketch the graph of the function . Your sketch should address: a. An analysis of : it's domain, intercepts, end behavior, and any asymtotes. b. An analysis of : the critical points, the extrema and classification, and each region of increase or decrease. c. An analysis of : the points of inflection (
2. Use calculus to sketch the graph of the function . Your sketch should address: a. An analysis of : it's domain, intercepts, and end behavior. b. An analysis of : the critical points, the extrema and classification, and each region of increase or decrease. c. An analysis of : the points of inflection, and the concavit
1). Given the differential equation for 1. L[y]= y''+2by'+b2y = exp(-bx)/x2, x>0 ; a) Find the complementary solution of (1) by solving L[y] = 0. b) Solve (1) by introducing the transformation y[x]= exp(-bx) v(x). into (1) and obtaining and solving completely a differential equation for v(x) . Now identify the part
Please answer the following: 1. Find the general solution y(x)of the given differential equation dy/dx = (sqrt)(y + 1) 2. Differentiate the following function f(x) = x(ln(x))^2 3. Evaluate the following indefinite integral Integral (e^(-1/x^2))/(x^3) dx 4. Differentiate the following function g(t) = ta
I just want to see why a step in a proof that I'm trying to follow is true. It's probably pretty simple.
Solve the differential equation. (du)/(dt) = (3 + 3 u + t + tu) u = -1 + A
Which of the following is a solution of the given initial-value problem. y' + tan(x) y = 4 cos^2(x) y(0) = -4. on the interval -pi/2 < x < pi/2 A) y = 4 sin(x) - 4 cos(x) B) y = 4 cos(x) - 4 sin(x)cos(x) C) y = 4 sin(x)cos(x) + 4 cos(x) D) y = 4 sin(x)cos(x) - 4 cos(x) E) y = 4 sin(x) + 4
One model for the spread of a rumor is that the rate of spread is proportional to the product of the fraction y of the population who have heard the rumor and the fraction who have not heard the rumor: a) Write a differential equation that is satisfied by y ( use k for the constant of proportionality) dy/dt = b) Solve t
Investments Morgan has $50,000 to invest and wants to receive $5000 interest the first year. He puts part in CD's earning 5.75%APY, part in bonds earning 8.75%APY and the rest in a growth fund earning 14.6% APY. How much should he invest at each rate if he puts the least amount possible in the growth fund? Mixing Acid Solu
1. In the following, represent the situation pictorially and deduce the governing 1st order differential equations and initial condition for the quantity in question. a) A tank, containing 300 gallons of pure water initially, is emptied out in the following fashion. A salt solution of concentration ½ lb of salt per gallon is
Please see the attached file for the fully formatted problems. 1. Given satisfying , ; π ; find 2. Given such that , ; list all possible solutions. For which of these does ?; ? 3. Suppose for it is known that Where "a" is a parameter. Determine the value of this parameter which ensure the existence
Please see the attached file for the fully formatted problems. keywords: burger's, burgers
Find the area of the surface obtained when the graph of y = x2, 0 ≤ x ≤ 1, is rotated around the y-axis. Find the volume of the solid that is generated by rotating the region formed by the graphs of y = x2, y = 2, and x = 0 about the y-axis. A 100-ft length of steel chain weighing 15 lb/ft is hanging
Looking for a calculation that given a latitude and longitude can return a search radius Here is the issue: I have a table of zip codes with their corresponding longitude and latitude values. For any given zip code, I need all of the zip codes in a 10 mile search radius. How would I set up the calculations to perform such a t
1. Solve: x*(dy/dx) - y = 2(x^2) * y 2. General solution for: dy/dx = ((x^2) + 1)/(2 - y) then particular solution for y = 4, x = - 3
Please see the attached file for the fully formatted problems. Find the inverse laplace transform of these Find the laplace transform of these Equate the coefficients for A,B and C
Evaluate ∫(log3x / 2x) (dx) R is bounded below by the x-axis and above by the curve y = 2cosx, Figure 11.1. Find the volume of the solid generated by revolving R around the y-axis by the method of cylindrical shells 0(< or =) x(< or =) pi/2 Find limx→∞ ( 3x-2/3x+2 )^x
R is the region that lies between the curve (Figure 15.1) and the x-axis from x = -3 to x = -1. Find: (a) the area of R, (b) the volume of the solid generated by revolving R around the y-axis. (c) the volume of the solid generated by revolving R around the x-axis. y=1 / x^2+4x+5
See the attachment. Solve the initial value problem.... Evaluate by interpreting the limit of Riemann sums... Find the integral....
The function of y(x) satisfies the differential equation and the initial condition y(1)=1. Firstly solve the equation to get an exact value then use Euler's method to obtain the value of y(2). Compare this value with the analytical value and discuss how the approximate value obtained by Euler's method may be improved. P
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: a) What is the maximum height attained by the ball? b) When and with what impact speed does the ball hit the ground? y(t)= -16t^2+ 80t+ 96 Find the interval on which the function is
Please see the attached file for the fully formatted problems. Question 1 Find ∫ x3+4 ________________________________________x2 dx Question 2 Solve the initial value problem: dy ________________________________________dx = x^/¯(9+x2) ; y(-4) = 0 Question 3 Figure 3.1 f(x) = x2+3 Figure 3.2
Find the maximum and minimum values attained by the function on the interval [0, 2]. h(x)=x-1/x+1 The equation has three distinct real roots. Approximate their locations by evaluating f at -2, -1, 0, 1, and 2. Then use Newton's method to approximate each of the three roots to four-place accuracy f(x)= x^3- 3x+ 1
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Set up but do not solve a differential equation that models the amount of salt in the tank for the following: A tank, having a capacity of 700 liters, initially contains 3 kilograms of salt dissolved in 100 liters of water. At time t=0, a solution containing 0.4 kilograms of salt per liter flows into the tank at a rate of 3 lite
Compute the 1-dimensional FT of 1/(1+x^2)^k by applying the calculus of residues.
Write the equation in terms of a rotated x'y'-system using q, the angle of rotation. Write the equation involving x' and y' in standard form. x2 + 2xy + y2 - 8x + 8y = 0; q = 45° x'2 = -4sqrt2y'2 x'2 = -4sprt2y' 3x'2 - 4sqrt2x'y' + y'2 = 0 2x'2 - sqrt2x'y' + 2y'2 = 0
Please see the attached file for the fully formatted problems.