. Differential and integral calculus. ave upward below the ar-axis and convex upward above the ^-axis. 2. Show that the hyperbola xy = m is concave upward inthe first angle and convex upward in the third angle. d2y 2 7ti Here » = !?? 3. Show that 3 a2y — Xs -+- 3 ax2 — 6 az = o has a point ofinflexion at (a, % a), and that the curve is convex upward on theleft of this point and concave upward on the right. 176 Differential Calculus 4. Examine the witch y = — —- for points of inflexion. Points of inflexion [ —=a, -a\ [ — —=a, -a\ VV3 2 / V V3 2 / 5. Examine for direction of curvature : (a) x2 +
. Differential and integral calculus. ave upward below the ar-axis and convex upward above the ^-axis. 2. Show that the hyperbola xy = m is concave upward inthe first angle and convex upward in the third angle. d2y 2 7ti Here » = !?? 3. Show that 3 a2y — Xs -+- 3 ax2 — 6 az = o has a point ofinflexion at (a, % a), and that the curve is convex upward on theleft of this point and concave upward on the right. 176 Differential Calculus 4. Examine the witch y = — —- for points of inflexion. Points of inflexion [ —=a, -a\ [ — —=a, -a\ VV3 2 / V V3 2 / 5. Examine for direction of curvature : (a) x2 + / = a2. (b) x2 = 2 py. (c) a7y2 - 62x2 = cPb\ 6. Examine for points of inflexion : (a) y = 2 xz — 3 x2 — \2 x -\- 12. (flj=2Jt5- 11 X2 + I 2 JC 4 It). (<:) jy = a:3 — 3 x2 + 1.(</) _) = 2 jc3 — 24 jc2 + 2 j^ — CURVES. 129. A polar curve is convex or concave to the pole at apoint according as the tangent to the curve at the point does,or does not, lie on the same side of the curve as the
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Keywords: ., bookcentury1900, bookdecade1910, booksubjectcalculu, bookyear1918
