### Find ds/dr for the curves: (a) r = a? (b) r = a/?

Tangent and Normal (III) (Differential Calculus) Find ds/dr for the curves: (a) r = a? (b) r = a/? See attached file for full problem description.

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Tangent and Normal (III) (Differential Calculus) Find ds/dr for the curves: (a) r = a? (b) r = a/? See attached file for full problem description.

Tangent and Normal (II) (Differential Calculus) Find ds/d? for the curves : (a) r2 = a2cos2? (b) rn = ancosn? See attached file for full problem description.

Find the General Solution of the equations. (a) r = a2t (b) r - 3as + 2a2t = 0 where r = ∂2z/∂x2 , s = ∂2z/∂x∂y, t = ∂2z/∂y2 (c) (2D2 + 5DD′ + 2D′2)z = 0 (d) ∂3z/∂x3 - 3∂3z/∂x2∂y + 2∂3z/∂x∂y2 = 0

I am having difficulties gaining a solution for the following differential equation of x'=2t3 -6t2 + t1/2. Could I please get assistance with detailing my solution.

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Please see attached file for various questions in Calculus. Thank you for your help.

Laplace Transformation Question. Please see attachment.

Laplace Transformations See attached for questions

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Dont really want you to give me answer, just thoery on how to complete these type of problems. Word problem with calculus Thank You (See Attached)

Please respond with a Microsoft Word document. Thank you. Please see attachment for actual questions and full formulas. 1. Decide whether Rolle's Theorem can be applied to on the interval [-1,3]. If Rolle's Theorem can be applied, find all the values, c, in the interval such that . If Rolle's Theorem cannot be a

Please respond with a Microsoft Word document with the answers written in standard text. Thank you. Series of Various Calculour Questions Attached.

Using covolution, find the solution of the differential eq y"+4y'+13y=(1/3)e^(-2t)sin3t y(0)=1, y'(0)=-2

Consider the forced harmonic oscillator: y'' + by' + ky = g(t) + y0 where the forcing is made up of two parts, constant forcing (y0) and forcing (g(t)) that changes over time. a) Let w(t) = y(t) - y0/k. Rewrite the forced harmonic oscillator equation in terms of the new variable w. b) In what ways are the solutions of the t

Please see attached

Please see the attached file for the fully formatted problem. Find a general solution on (-pi/2, pi/2) to y'' + y = tan x given that S secx dx = ln |sec x + tan x|.

Given that the differential equation y^n + p(x)y' + q(x)y = r(x) attached has three solutions of sin x, cos x and sin 2x. Find yh (yh is the corresponding homogeneous solution). See attachment for better formula representation.

Given that the differential equation y^n + p(x)y' + q(x)y =0 has two solutions x^2 -x and x^3 - x. Use the Wronskian to find p(x). See attachment for better formula representation.

Find a general solution to the equation in the attachment

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Determine whether the following questions are linear or nonlinear. (a) yy''-y'=sin(x) (b)x^2y''-y'+y=cos(x)

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I attached the problems that I would like you to do. I have already completed these problems by myself, but would like to see if I did them correctly and would like to compare your answers with mine so that I know which problems I mastered and which I need to study up on. Thank you.

Attached is more clear 1. Distance from a a point to a curve: Find the shortest distances between the point (1,2,1) and a point on the curve r(t)= (1/t*i)+(lnt(t)*j)+(sqrt(t)*k) 2. Distance from a point to a curve: Find the maxmium distances from the point (1,2,-1) to a point on the curve of intersection of the plane z=(