. Differential and integral calculus, an introductory course for colleges and engineering schools. and show that the tangents at these points are double tangents. Example 2. p = asin^0. The greatest value p can have is a, and therefore the curve lies entirelywithin a circle whose center is the poleand radius a. As 0 varies from 0 to5 7T, 1 0 varies from 0 to ic, and P first in-creases from 0 to a,(d = ifh and then decreases to 0 again (0 = 5ir). When0 is — and varies from 0 to — 5tt, thesame curve is traced but in the oppositedirection. The student should trace thecurve by plotting the points
. Differential and integral calculus, an introductory course for colleges and engineering schools. and show that the tangents at these points are double tangents. Example 2. p = asin^0. The greatest value p can have is a, and therefore the curve lies entirelywithin a circle whose center is the poleand radius a. As 0 varies from 0 to5 7T, 1 0 varies from 0 to ic, and P first in-creases from 0 to a,(d = ifh and then decreases to 0 again (0 = 5ir). When0 is — and varies from 0 to — 5tt, thesame curve is traced but in the oppositedirection. The student should trace thecurve by plotting the points for which. = 0, 3jr 4 using a table of natural sines to calculate p. A better way is to use polar-coordinate paper and the methods explained in analytic geometry. Problem. Determine at the points where the curve of example 2 cutsOX and OY. Ans. Two of the values of are 85° 17 and 81° 44. 99. Exercises. Draw the following curves, calculating 4> forimportant points: 1. p = a sin figure shows but one loop; draw the others. Find the coor-dinates of the points where thetangents are parallel to the axisof the loop, and thus find thegreatest width of the loop. Ans. to last, .544 a. 2. p = a sin2 width of each loop at widest part. Ans. .77 a. 3. p = asin^ curve has two double Ans. .544 a.
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Keywords: ., bookcentury1900, bookdecade1910, booksubjectcalculu, bookyear1912
