学进去

给定整数，如果非空集合满足：
一：，，
二：，，若，则，那么称集合为“减集”.
(1)是否为“减0集”？是否为“减1集”？
(2)是否存在“减2集”？如存在，求出所有“减2集”；如不存在，请证明.
(3)是否存在“减1集”？如存在，求出所有“减1集”；如不存在，请证明.

已知函数，其中.
（1）若在处的切线与轴的交点为，求的值；
（2）设函数，当时，试讨论的单调性.

17到19世纪间，数学家们研究了用连分式求解代数方程的根，并得到连分式的一个重要功能：用其逼近实数求近似值．例如，把方程改写成①，将再代入等式右边得到，继续利用①式将再代入等式右边得到……反复进行，取时，由此得到数列，，，，，记作，则当足够大时，逼近实数．数列的前2024项中，满足的的个数为（参考数据：）

A．1007

B．1009

C．2014

D．2018

已知函数
(1)当时，求在点处的切线方程；
(2)若对恒成立，求实数的取值范围
(3)若有3个零点，其中，求实数的取值范围，并证明．

阅读下面材料，根据其内容和所给段落开头语续写两段， 使之构成一篇完整的短文。

Reese Osterberg, a 10-year-old girl, is a big fan of the baseball team San Francisco Giants and Little League. When the girl lost her home in Fresno County, California, to one of the largest wildfires in state history early last fall, she had a very pressing concern: Did anyone grab her cherished baseball cards?

Unfortunately, no one had. Her mom recalled that the roaring fire seemed to devour (吞噬) everything in their yard. Danger was definitely around them. With a houseful of kids and dogs and a farm’s worth of horses to evacuate, if they didn’t hurry up, the consequences would be unimaginable. So at the extremely urgent moment, the whole family totally forgot her cards am id the dangerous situation. Naturally, the enthusiastic fan of San Francisco Giants and Little League was upset. When she watched the Giants on TV, she would lay out each player’s card on the floor in his corresponding field position. “I like baseball cards because they are pictures of people doing happy stuf — doing what they love, and what I love”, says Reese.

Reese’s loss deeply touched the hearts of the warmhearted firefighters from Fresno County Fire Department. They decided to do something to help the upset kid. Before long, they posted her story on its   Face-book page with a plea to help Reese regain her baseball card collection. The story, in turn, touched the heart of kind Kevin Ashford, a longtime baseball collector, who was more than willing to seize the opportunity to do good.

Ashford knew exactly where Reese could find replacement cards: in his garage. He had more than 25,000 in his collection, with a ball park value of $35,000 to $50,000. Ashford had been thinking about selling them when he happened to read the fire department’s post. “I wasn’t really doing anything with them,” says Ashford. “I thought I could take care of this problem rather quickly.”

注意：
1. 续写词数应为 150 左右；
2. 请按如下格式在答题卡的相应位置作答。

Ashford immediately responded to the post.

—————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————

Reese has gotten so many cards from Ashford and she decided to share these cards with other kids.

—————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————

若函数与区间同时满足：①区间为的定义域的子集，②对任意，存在常数，使得成立，则称是区间上的有界函数，其中称为函数的一个上界．（注：涉及复合函数单调性求最值可直接使用单调性，不需要证明）
(1)试判断函数，是否是上的有界函数；（直接写结论）
(2)已知函数是区间上的有界函数，求函数在区间上的所有上界构成的集合；
(3)对实数进行讨论，探究函数在区间上是否存在上界？若存在，求出的取值范围；若不存在，请说明理由．

假定你是高一新生李华，你的英国笔友弗瑞德 (Fred) 来信询问你入学第一天的情况。 请你给他回一封信，内容包括：
1. 介绍学校环境；
2. 谈谈对老师和同学的印象；
3. 你对高中生活的信心。
注意：1 词数 80 词左右；2 可以适当增加细节，使行文连贯。

阅读下面材料，根据其内容和所给段落开头语续写两段，使之构成一篇完整的短文。

Teen Becomes A Local Hero

When Sydney Raley headed into her weekend shift on Saturday, December 18, she likely expected to do more of the same: Stand at the drive-through window, take orders over the headset, and hand each customer their meal with a smile.

In fact. that’s exactly how it started. Sydney Raley has been working at MC Donald’s for about seven months and so far, it’s been her typical after-school job. The day had been mostly normal -making coffee, making drinks, and going into the lunch rush.

But a few hours into her shift. things took a dramatic turn. After handing a customer some of their food, Sydney let them know that more would be coming as soon as it was ready. But just seconds later, she noticed a terrible look of panic spread across the woman’s face. Then came the coughing. She was coughing like crazy and was speechless. Her daughter was in the passenger seat and looked extremely confused and frightened.

Sydney immediately knew she was choking. The first aid training Sydney received more than four years ago hit her. Most 15-year-olds might panic at the sight of this. But not Sydney. Instead, the teen remained calm and quickly shouted to both her manager and the woman’s daughter to dial 911. Then, she dove through the drive-through window and came to the rescue.

The teen pushed the driver’s side door forcefully open and got the choking woman to her feet. Then she dug down deep into her memory bank to recall everything she learned from her Red Cross babysitter class-which she’d taken four years earlier. All that training of how to use the Heimlich maneuver(哈姆立克急教法)immediately kicked in. Still, she had never actually had to use the life-saving technique before, and after a few tries, it wasn’t quite working. Luckily, another customer was just a few feet away in the parking lot.

注意：
1.续写词数应为150左右；
2.请按如下格式在答题卡的相应位置作答。
She shouted to that man for assistance.
______________________________________________________________________________________________________________________________________________________________________________________________
The story has made headlines throughout the country.
______________________________________________________________________________________________________________________________________________________________________________________________

如图，设P是上的动点，点D是点P在x轴上的投影，Q点满足（）．

(1)当点P在圆上运动时，求点Q的轨迹C的方程；
(2)若，设点，A关于原点的对称点为B，直线l过点且与曲线C交于点M和点N，设直线AM与直线BN交于点T，设直线AM的斜率为，直线BN的斜率为．
（i）求证：为定值；
（ii）求证：存在两条定直线、，使得点T到直线、的距离之积为定值．

如图，在三棱锥中，为等边三角形，三棱锥的体积为，则三棱锥外接球的表面积为__________.