in to besde low gansz Newton and Leibniz are credited as being the co-founders of calculus. A Source Book in Mathematics (D.E. Smith) includes a section from Newton's calculus papers. Read Newton's "On Fluxions" and work through his "fluxion" (i.e. derivative) for x". Newton considers the ratio (aniq E): bns blu (x+0)-x (x+o)n-xn Diw qugnibn (3 points) 1) Work through Newton's derivation to show that x2 = -2x-3 by expanding (x + 0)-2 using dx e with n = -2.01) infinite series and then simplifying the ratio given above with n = -2. 0 = x[(LE)ST - (SE)II] + (02)S! - (SE)01 (2) oldsnsy x 9dt stenimils (zibubong 26 zeon1919 0982919x9.9.1) x lo zinsipiteco 08 $1+08 SS 11+SE 15-011291 'sindis. 16 svins uoy lizmu sbla bnst gmU I bos 01-18 2) Newton also finds the fluxion of a multi-variable function by replacing x, y and z with (x+o), (y+o) and (z+o), respectively. He subtracts the original equation from the second equation and divides by o before letting o "be diminished infinitely." Work through Newton's approach to find the fluxion of the equation 4x - 3yz += 0. (Don't be intimidated by the, just find a 1 - Z 1 1 common denominator and compute and it all will work out.) z+o Z upe vtilamiz Sai xhem ingilt903 9f toxins srit 2039d sldcvloza matay? ad 263 aldi ni S