解题方法
1 . 已知函数
.
(1)求函数的定义域;
(2)判断函数的奇偶性,并给予证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fb402b4847c5bc1caec9ff83958d06c.png)
(1)求函数的定义域;
(2)判断函数的奇偶性,并给予证明.
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解题方法
2 . 回答下面两题:
(1)化简求值:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2623ca2935d6bebbf873a68dbf81e4be.png)
(2)已知
,求
(1)化简求值:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2623ca2935d6bebbf873a68dbf81e4be.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9a7de5b70003502e40b95b3b7d3d933.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b021030a58baefb6ba50359530762d2b.png)
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3 . 设
是公比大于1的等比数列,
为数列
的前
项和.已知
,且
、
构成等差数列,令
.
(1)求数列
的通项公式;
(2)令
,求数列
的前
项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ccdc17b603871d20843ffccca2df0ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aadfe0800c4dc2fe3434c488cf3fe9ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0462c9dc4a0bd08a0ec1cc07f1d2f3e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/131d12bb9ea1eb58c7f0721a291598b0.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8f50ac3b1d543e1a09eb9e84da4f5a0.png)
(2)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daf35e622dc7630e7f5d056b1b6af1df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
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4 . 已知集合
,其中实数
是常数.
(1)求集合A与集合
;
(2)若对任意的
,都有
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ea3ac2f45b27e6f22bddfdc1ca0ef72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(1)求集合A与集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(2)若对任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e23af61cd402b3789af2401bde9cbefe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ed006b944ea64f970fee46e2f558467.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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5 . 计算:
(1)
;
(2)
.
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8da2b31b4d8c7ef16c218d6d23cc534.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20856e9f876a3793bd2a56627a88cc63.png)
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解题方法
6 . 已知函数
(
且
)为奇函数.
(1)求实数
的值;
(2)若
,求函数
的解析式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8788e0cbf25b5b7ab437952fc1e7315.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c400a615a16a1662de98dfb4e49d58d3.png)
(1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c30e01790ac61851c453cbef2d5245d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
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7 . 计算:
(1)
;
(2)
.
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a55057f6c840e1e378e9ee62e01c93a.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a247a58c19921f43de886bdcf7ad7b8.png)
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8 . 已知函数
(其中
,
).
(1)求它的定义域;
(2)求它的单调区间;
(3)判断它的奇偶性;
(4)判断它的周期性,如果是周期函数,求出它的最小正周期.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64580ddd4451df005cbd072c5bac6ba1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c400a615a16a1662de98dfb4e49d58d3.png)
(1)求它的定义域;
(2)求它的单调区间;
(3)判断它的奇偶性;
(4)判断它的周期性,如果是周期函数,求出它的最小正周期.
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9 . 计算下列各式的值:
(1)
;
(2)
.
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cd39bf6ef245682c9a60042294d5721.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52c4ccd346562138dc660d807276b87e.png)
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解题方法
10 . 已知
为实数,设集合
.
(1)设集合
,若
,求实数
的取值范围.
(2)若集合
,求实数
的取值范围;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afbdb9295c1b5fa1a0ccbb9c4c5f9f19.png)
(1)设集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13efe1f6d9b5e55020f10ed39aa78c35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/caf22d7d1a965bda25168a233fb6290c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c27b6c1f267d7b820b64f5782c6466de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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