问题 填空题
下列说法:
①函数f(x)=lnx+3x-6的零点只有1个且属于区间(1,2);
②若关于x的不等式ax2+2ax+1>0恒成立,则a∈(0,1);
③函数y=x的图象与函数y=sinx的图象有3个不同的交点;
④函数y=sinxcosx+sinx+cosx,x∈[0,
π
4
]
的最小值是1.
正确的有______.(请将你认为正确的说法的序号都写上)
答案

对①,f(1)=-3,f(2)=ln2>0,∵f(-1)×f(2)<0,且f(x)在(1,2)上是增函数,∴函数在(1,2)内只有一个零点.故①正确;

对②关于x的不等式ax2+2ax+1>0恒成立⇒a=0或

a>0
△<0
⇒0≤a<1.故②不正确;

对③根据正弦线|sinx|≤|x|当且仅当x=0取“=”,∴只有一个交点,故③不正确;

对④设t=sinx+cosx=

2
sin(x+
π
4
),∴t∈[1,
2
],y=
t2-1
2
+t=
1
2
(t+1)2-1,∴函数的最小值是1.故④正确.

故答案是①④

阅读理解
Watching Movies for Your Summer
Garfield: A Tale of Two Kitties
——《加菲双猫记》
Hello, Garfield will meet you again on the screen. This time, America’s favourite cat Garfield travels to London. Garfield gets lost . However, he enjoys his new life in his new home. But danger is near him.
Superman Returns
——《超人归来》
How exciting to see Superman on the screen again. Like before, he is again saving the world. But his enemy, Lex Luther, is still planning to kill him so that he can control the world.
Pirates of the Caribbean: Dead Man’s Chest
——《加勒比海盗:聚魂馆》
Captain Jack Sparrow again appears on the screen. This time, he finds himself in a heavy debt(负债) to Davey Jones. The only way to get out of it is to find the Dead Man’s Chest. He asks his old friends for help and they start out to the sea.
(  )1. The story of Garfield in this movie happens in ______ .
      A. America     B. London      C. the sea       D. the world
(  )2. Why does Lex Luther plan to kill Superman?
     A. Because he tried to save the world.
     B. Because he never sees Superman on the screen.
     C. Because he finds it hard to like the story.
     D. Because he wants to control the world.
(  )3. What is the trouble for Captain Jack Sparrow this time?
A. He again appears on the screen. B. He turns to his friends for help.
C. He is in a heavy debt to Davey Jones. D. He finds the Dead Man’s Chest.
填空题