Classical Dynamics of Particles and Systems · Problem 4-5

Gravitation — Marion & Thornton

Physics — Mechanics · successive-approximation

Problem

Solve by a successive approximation procedure, and obtain a result accurate to four significant figures: (a) x+x2+1=tan⁡xx + x^2 + 1 = \tan x, 0≤x≤π/2\quad 0 \leq x \leq \pi/2 (b) x(x+3)=10sin⁡xx(x+3) = 10\sin x, x>0\quad x > 0 (c) 1+x+cos⁡x=ex1 + x + \cos x = e^x, x>0\quad x > 0 (It may be profitable to make a crude graph to choose a reasonable first approximation.)

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