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Calculus and Analysis

Sketching Contour Maps and Determining Radii for a Hemisphere

The hemisphere is given by f (x,y) = sqrt 64 - x^2 - y^2. Sketch a contour map for this surface using the level curves corresponding to c = 0,1,2,3,4,5,6,7,8 Since this is an example shown in the book, I can see that when c = 8 you draw a circle with a radius of 8 and when c = 0 you have a point at the center of the circle.

Infinite Sequences (20 problems)

Please see the attached file for the fully formatted problems. Please do problems 3 - 8, 10, 12, 14, 16 - 40 even, 42 ,44,45-49, 54 - 60 odd.

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.

Limits

Please answer the attached questions. On question #3 the last two mutliple choice options didn't scan they are: c.Yes, the limit exists, and is equal to -1. d. Yes, the limit exists, and is equal to 0.

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.

Brief 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

Identities

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