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Calculus and Analysis

Vector-valued function word problem.

At time t = 0 a baseball that is 5 feet above the ground is hit with a bat. The ball leaves the bat with a speed of 80 feet per second at an angle of 30 degrees above horizontal. a) How long will it take for the baseball to hit the ground? b) Use the result in part a to find the horizontal distance traveled by the ball. Ple

Bernoulli Equation and Capacitor Current

Find the general solution of the Bernoulli equation: dy/dx -y/x = (y^4 cosx/x^3) A fully charged capacitor is discharged and the current i(t) flowing through a series of RC circuit at time t satisfying the equation: 1540 di/dt +800i =0. Given that E=115 V, draw the complete RC circuit and sketch the current (i) waveform.

Comparisons of Radii of Convergence

Suppose and have radii of convergence R1 and R2, respectively, where R1 and R2 are non-zero real numbers. What can be said about the radius of convergence of the following series. Justify youtr answers, ? ? ? ? , where Please see the attached file for the fully formatted problems.

Present Value of Money and Calculus

Please answer the following questions: The Present value of money is the amount that you need to deposit now in order to have a desired amount sometime in the future . 1. What is the present value needed in order to have saved $60,000 in five years, given an annual interest rate of 7% compounded monthly? 2. What is the

Volume of revolution..

Consider the function x=12(y^2-y^3). Determine why revolving this curve about the x-axis has a different volume than revolving about a line y=1.

Differential Equations : Equations of Motion, Laplace Transforms

Refer to figure 2 in attachment. a) Write the equations of motion for the mechanical system.****PLEASE SHOW YOUR FREE-BODY FOR EACH MASS****THANKS B) Take the Laplace transform of these equations, arrange them in matrix form, solve for the displacement x2(t), and find the transfer function T(s)= X1(s)/F(s) C) Using the co

Length of a curve

Using the formula for the length of a curve y=f(x) from a to b L=∫√(1 + (dy/dx)²)dx Find the length of the curve: x=(y³∕6) + 1/(2y) from y=2 to y=3 Hint: 1 + (dx/dy)². is a perfect square

Identity Functions Detailed

Prove the given identity - Please explain in detail. 14. 2 cos x - 2 cos^3x = sin x sin 2x 16. cos (x-y)/cos x cosy = 1 tan x tany 20. sec x -cos x = sin x tanx 22. sin 2x = 1/tanx +cot 2x 23. If tan x = 5/12 and sin x>0 , find sin 2x 26. If sin x = -12/13 with pie <x<3pie/2, and sec y = 13/12 with 3 pi

Finding the Volume of Revolution Using the Shell Method

Using the shell method, find the volume of a solid generated by revolving about the y axis. The boundaries of the solid are: y=9x/&#8730;(x³+9) the x-axis the line x=3 Note: I received a solution to this problem from an OTA, but it appeared that the integration wasn't complete. I would like to see another OTA sol

Inverse Laplace Transforms and Convolution Integral

Find the inverse Laplace transform of the following: (a) 10/(s2+9) (b) 2e^-2s /(s+3) (c) .... (d) Find the inverse Laplace transform of F(s) using convolution integral where F(s) = .... Please see the attached file for the fully formatted problems.

Limits and L'Hopital's Rule (34 Problems with High Quality Solutions)

Find the limits using L'Hopital's rule where appropriate. If there is a more elementary method, consider using it. If L'Hospital's rule does not apply explain why. 1) lim as x approaches -1 (x^2 -1) / (x + 1) 2) lim as x approaches -1 (x^9 -1) / (x^5 - 1) 3) lim as x approaches -2 (x+2) / (x^2 +3x + 2) 4) lim as x approa

Graphing, Translation, Reflection, Domains, Limits, Derivatives

For the following graph the given functions on a computer screen, how are these graphs related? 1) Y=2^x, y=e^x, y=5^x, y=20^x 2) Y=3^x, y=10^x, y=(1/3)^x, y=(1/10)^x _______________________________________________________________________ Make a sketch of the function. 7) y=4^x-3 8) y=-2x^-x 9) y=3-e^x 13)