Comet distance from Sun in AU Figure 11-5. Brightness-versus-distance graphs for three hypothetical comets.
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This equation has the single root x = 1, which occurs with multiplicity 3. We can plug x = 1 into either of the original functions to get the y-value. Let s use the first function. That gives us y = 2x 3 + x 2 + x 4 = 2 13 + 12 + 1 4 =2 1+1+1 4 =2+1+1 4 =0 The solution to the system is therefore (x,y) = (1,0), with multiplicity 3. 10. First, we check (1,0) in the first original two-variable cubic: 4x 3 + 2x 2 + 2x 2y 8 = 0 4 1 + 2 12 + 2 1 2 0 8 = 0 4 1+2 1+2 0 8=0 4+2+2 8=0 8 8=0 0=0
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pain. Perception of touch and pinprick are reduced in the territory of the nerve; there is no weakness of the quadriceps or diminution of the knee jerk. The symptoms are characteristically worsened in certain positions and after prolonged standing or walking. Occasionally, for an obese person, sitting is the most uncomfortable position. Obesity, pregnancy, and diabetes mellitus may be contributory factors. Most often the neuropathy is unilateral; Ecker and Woltman found only 20 percent of their cases to be bilateral. Most of our patients with meralgia paresthetica request no treatment once they learn of its benign character. Weight loss and adjustment of restrictive clothing or correction of habitual postures that might compress the nerve are sometimes helpful. A few with the most painful symptoms have demanded a neurectomy or section of the nerve, but it is always wise to perform a lidocaine block rst, so that the patient can decide whether the persistent numbness is preferable. In one specimen of nerve obtained at operation, we found a discrete traumatic neuroma. Hydrocortisone injections at the point of entrapment may have helped in a few cases. Obturator Nerve This nerve arises from the third and fourth and to a lesser extent the second lumbar roots. It supplies the adductors of the thigh and contributes to the innervation of the internal and external rotators. The adductors have the added function of exing the hip. The nerve may be injured by the fetal head or forceps during the course of a dif cult labor or compressed by an obturator hernia. Rarely, it is affected with diabetes, polyarteritis nodosa, and osteitis pubis and by retroperitoneal spread of carcinoma of the cervix, uterus, and other tumors (Rogers et al). Femoral Nerve This nerve is formed from the second, third, and fourth lumbar roots. Within the pelvis it passes along the lateral border of the psoas muscle and enters the thigh beneath Poupart s ligament, lateral to the femoral artery. Branches arising within the pelvis supply the iliacus and psoas muscles. Just below Poupart s ligament the nerve splits into anterior and posterior divisions. The former supplies the pectineus and sartorius muscles and carries sensation from the anteromedial surface of the thigh; the posterior division provides the motor innervation to the quadriceps and the cutaneous innervation to the medial side of the leg from the knee to the internal malleolus. Following injury to the femoral nerve, there is weakness of extension of the lower leg, wasting of the quadriceps muscle, and failure of xation of the knee. The knee jerk is abolished. If the nerve is injured proximal to the origin of the branches to the iliacus and psoas muscles, there is weakness of hip exion. The adductor of the thigh (innervated by the obturator nerve) is spared, distinguishing femoral neuropathy from an L3 radiculopathy. The most common cause of femoral neuropathy is diabetes. The nerve may also be involved by pelvic tumors. Not uncommon is injury of the nerve during pelvic operations. Usually this is the result of improper placement of retractors, which may compress the nerve directly or indirectly by undue pressure on the psoas muscle. Bleeding into the iliacus muscle or the retroperitoneum, observed in patients receiving anticoagulants and in hemophilia patients, is a relatively common cause of isolated femoral neuropathy (Goodfellow et al). The presenting symptom of iliacus hematoma is pain in the groin spreading to the lumbar region or thigh, in response to which the patient assumes a characteristic posture of exion and lateral rotation of the hip. A palpable mass in the iliac fossa and the signs of femoral nerve compression (quadriceps weakness and loss of knee jerk) follow in a day or two. Infarction
Figure 14-1 The Cartesian plane consists of two
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