An elementary treatise on curve tracing . EXAMPLES OF APPROXIMATION 35 PLATEThe first approximation gives ill. {y-x){y-2x) = (d; .. y = x, or 2x. (i) Commencing with y = x for the second approximation, 4a^x^y — a?x^y^ y = x- a%y — 2x) = 03 + -^. ^ ,, ,, . , 1 4a?% —aj^-V^ Qx^ — 2x^y^ For the third, y = x--~^ ^ 5? iTx ^ a^ y — 2x a\y — zx) a Sx^ a^ , 3x^ ,15a)^ , 4x0a^ a* a- (ii) Commencing with i/ = 2ic for the second approximation, « 1 x^y(^x — y)y = 2x —5 —^-^ ^^- 2/-a^ = 2^-^. For the third, _^ 1 x^4,x-{y-2xf} 2x%Sx^-y^) ^ d^ y — x a\y — x) 1 ofiAx , 2a;« a^ /, 4£c-\ a^«;( 1 5- _ 4cc^ 16a;^
An elementary treatise on curve tracing . EXAMPLES OF APPROXIMATION 35 PLATEThe first approximation gives ill. {y-x){y-2x) = (d; .. y = x, or 2x. (i) Commencing with y = x for the second approximation, 4a^x^y — a?x^y^ y = x- a%y — 2x) = 03 + -^. ^ ,, ,, . , 1 4a?% —aj^-V^ Qx^ — 2x^y^ For the third, y = x--~^ ^ 5? iTx ^ a^ y — 2x a\y — zx) a Sx^ a^ , 3x^ ,15a)^ , 4x0a^ a* a- (ii) Commencing with i/ = 2ic for the second approximation, « 1 x^y(^x — y)y = 2x —5 —^-^ ^^- 2/-a^ = 2^-^. For the third, _^ 1 x^4,x-{y-2xf} 2x%Sx^-y^) ^ d^ y — x a\y — x) 1 ofiAx , 2a;« a^ /, 4£c-\ a^«;( 1 5- _ 4cc^ 16a;^ 2a;0 Ex. 4. To approximate to the sohUions of the equationtanx = x, the unit being the unit of circular measure. Draw the curve y = tan x, and let the tangent at 0, y = x,meet the curve in ...P, O, P, Q,... , fig. 17, plate II. 36 EXAMPLES OF APPROXIMATION PLATE III. The figure shews that, since the branches of the curve are all similar, the abscissae of the points P, Q, R, etc. arenearer and nearer to the valu
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