Найти пределы функции: lim x->0 arcsin3x/5x

Найти пределы функции:
lim x->0 arcsin3x/5x
- Предмет:
  Математика
- Автор:
  india46
- 6 лет назад

Ответы 1

Так как при x⇒0 arcsin(3*x)⇒0 и 5*x⇒0, то в данном случае имеем неопределённость вида 0/0. Для нахождения предела применим правило Лопиталя. Так как (arcsin(3*x))'=3/√(1-9*x²), а (5*x)'=5, то lim x⇒0 (arcsin(3*x))/(5*x)=lim x⇒0 1/5*3/√(1-9*x²)=1/5*3=3/5. Ответ: 3/5.
- Автор:
  mauricio721
- 6 лет назад
- 0
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5 Famous Thinkers and Their Inspiring Daily Rituals
Many find it interesting to glimpse inside the lives of famous thinkers in an effort to understand where such thought and intelligence is rooted. In that vein, here is a peek into the routines and rituals that writers, philosophers, and statesmen have depended on to keep their work on track and their thoughts flowing. Whether you need inspiration to make it through the next college semester or are working on a future best-selling novel, explore these daily rituals you may want to incorporate into your life.
1. Haruki Murakami. This popular Japanese novelist sticks to a specific daily schedule that begins at 4:00 when he awakes. He writes for five or six hours, then either runs 10k or swims 1500 meters (or sometimes, both). After his workout, he reads and listens to music until he goes to bed at 9:00. Murakami claims that writing a novel requires both the physical and mental strength that his routine provides.
2. Charles Darwin. In his middle and later years, Darwin stuck to a very rigid schedule that started at 7:00 in the morning with a short walk, then breakfast. He would then work throughout the morning. Lunch, at 12:45, was his biggest meal of the day. His afternoon was also scheduled and consisted of two walks, reading, and backgammon. Darwin could not tolerate much socializing, and kept it to a maximum of 30 minutes at a time.
3. Winston Churchill. While Churchill’s routine may not be for everyone, it seemed to revolve around lots of food and drink. He would rise at 7:30 and stay in bed until 11:00 where he would eat breakfast, read several newspapers, and dictate to his secretaries. When he finally got out of bed, he would bathe, take a walk outside, then settle in to work with a weak whisky and soda. Lunch began at 1:00 and lasted until 3:30, after which he would work or play cards or backgammon with his wife. At 5:00 he napped for an hour and a half, then bathed again and got ready for dinner. Dinner was considered the highlight of his day, with much socializing, drinking, and smoking that sometimes went past midnight. After his guests left, he would then work for another hour or so before heading to bed.
4. Aldous Huxley. This famous thinker and writer would start early each day sharing a breakfast with his wife. He would work uninterrupted until lunchtime. After lunch, he and his wife would go for a drive or a walk, then he would return to work again from 5:00 to 7:00, then have dinner. After dinner, his wife would read to him until almost midnight. Due to an eye illness early in life that left Huxley with very poor eyesight, he relied heavily on his wife to do many activities for him besides reading. She often typed his manuscripts and was even reported to have cut his steak for him at dinner.
5. James Thurber. Another writer with difficulties seeing, Thurber would often compose his work in his head at almost anyplace he found himself. His wife would recognize the look in his eyes and interrupt him mid-paragraph while they were socializing at a party, and his daughter saw him retreat into his private world over dinner. His method later in life was to spend all morning composing his text in his head, then between 2:00 and 5:00 he would dictate about 2,000 words to his secretary.
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Найти пределы функции: lim x->0 arcsin3x/5x

Ответы 1

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Найти пределы функции:
lim x->0 arcsin3x/5x