设函数连续且恒大于零
,,
其中,,
讨论在区间内的单调性;
证明当时,
___________.
设函数具有连续导数,在围绕原点的任意分段光滑简单闭曲线上,曲线积分的值恒为同一常数.
证明:对右半平面内的任意分段光滑简单闭曲线,有;
求函数的表达式.
____________.
比较与的大小,说明理由.
设,求极限
Psychologists are finding that hope plays a surprisingly vital role in giving people a measurable advantage in realms as (1) _________ as academic achievement, bearing up in tough jobs and coping with (2) _________ illness. And, by contrast, the loss of hope is turning out to be a stronger sign that a person may (3) _________ suicide than other factors long thought to be more likely risks.
“Hope has proven a powerful predictor of (4) _________ in every study we’ve done so far,” said Dr. Charles R. Snyder, a psychologist who has devised a (5) _________ to assess how much hope a person has.
For example, in research with 3,920 college students, Dr. Snyder and his (6) _________ found that the level of hope among freshmen at the beginning of their first semester was a more (7) _________ predictor of their college grades than were their S.A.T. scores or their grade point (8) _________ in high school, the two measures most commonly used to predict college performance. (9)“____________________________,” Dr. Snyder said. “When you compare students of equivalent intelligence and past academic achievements, what sets them apart is hope.”
In devising a way to assess hope scientifically, Dr. Snyder (10) ____________________________. “That notion is not concrete enough, and it blurs two key components of hope,” Dr. Snyder said.(11)“____________________________.”