高数概念[基础知识] 因式分解公式:a^{n}-b^{n}=(a-b)(a^{n-1}+a^{n-2}b+\cdots+ab^{n-2}+b^{n-1})(n为正偶数时(a^{n}-b^{n}=(a+b)(a^{n-1}-a^{n-2}b+\cdots+ab^{n-2}-b^{n-1})(n为正奇数时)a^{n}+b^{n}=(a+b)(a^{n-1}-a^{n-2}b+\cdots -ab^{n-2}+b^{n-1})二项式定理:(a+b)^{n}= \sum _{k=0}^{n}C_{n}^{k}a^{k}b^{n-k} 不等式：(1)a，b位实数，则\Phi 2|ab| \le a^{2}+b^{2};\varnothing |a \pm b| \le |a|+|b|;\circled {3}|a|-|b| \le |a-b|.(2)a_{1},a_{2}, \cdots ,a_{n}>0, 则 \frac {a_{1}+a_{2}+\cdots+a_{n}}{n} \ge \sqrt [n]{a_{1}a_{2} \cdots a_{n}} 取整函数:x-1<[x] \le x 三角函数和差化积；积化和差(7)：\sin \alpha+\sin \beta =2(\sin \frac { \alpha+\beta }{2})(\cos \frac { \alpha - \beta }{2})\sin \alpha \cos \beta = \frac {1}{2}(\sin \frac { \alpha+\beta }{2}+\cos \frac { \alpha - \beta }{2})\sin \alpha - \sin \beta =2(\cos \frac { \alpha+\beta }{2})(\sin \frac { \alpha - \beta }{2})\cos \alpha \cos \beta = \frac {1}{2}(\cos \frac { \alpha+\beta }{2}+\cos \frac { \alpha - \beta }{2})\cos \alpha+\cos \beta =2(\cos \frac { \alpha+\beta }{2})(\cos \frac { \alpha - \beta }{2})\sin \alpha \sin \beta =- \frac {1}{2}(\cos \frac { \alpha+\beta }{2}- \cos \frac { \al

数学(二)必背公式[基础知识] 因式分解公式:a^{n}-b^{n}=(a-b)(a^{n-1}+a^{n-2}b+\cdots+ab^{n-2}+b^{n-1})(n为正偶数时(1)a^{n}-b^{n}=(a+b)(a^{n-1}-a^{n-2}b+\cdots+ab^{n-2}-b^{n-1})(n为正奇数时)a^{n}+b^{n}=(a+b)(a^{n-1}-a^{n-2}b+\cdots -ab^{n-2}+b^{n-1})二项式定理:[(a+b)^{n}= \sum _{k=0}^{n}C_{n}^{k}a^{k}b^{n-k} 不等式：(1)a,b位实数,则\circled {4}2|ab| \le a^{2}+b^{2};\circled {2}|a \pm b| \le |a|+|b|;\circled {3}|a|-|b| \le |a-b|.(2)a_{1},a_{2}, \cdots ,a_{n}>0, 则 \frac {a_{1}+a_{2}+\cdots+a_{n}}{n} \ge \sqrt [n]{a_{1}a_{2} \cdots a_{n}} 取整函数:\mid x-1<[x] \le x 三角函数和差化积;积化和差(7):\sin \alpha+\sin \beta =2(\sin \frac { \alpha+\beta }{2})(\cos \frac { \alpha - \beta }{2})\sin \alpha \cos \beta = \frac {1}{2}(\sin \frac { \alpha+\beta }{2}+\cos \frac { \alpha - \beta }{2})\sin \alpha - \sin \beta =2(\cos \frac { \alpha+\beta }{2})(\sin \frac { \alpha - \beta }{2})\cos \alpha \cos \beta = \frac {1}{2}(\cos \frac { \alpha+\beta }{2}+\cos \frac { \alpha - \beta }{2})\cos \alpha+\cos \beta =2(\cos \frac { \alpha+\beta }{2})(\cos \frac { \alpha - \beta }{2})\sin \alpha \sin \beta =- \frac {1}{2}(\cos \frac { \alpha+\beta }{2}

导数公式:(tgx)'=sec^{2}x(\arcsin x)'= \frac {1}{ \sqrt {1-x^{2}}}(ctgx)'=-csc^{2}x(\arccos x)'=- \frac {1}{ \sqrt {1-x^{2}}}(secx)'=secxtgx(cscx)'=-cscxctgx(\arctan x)'= \frac {1}{1+x^{2}}(a^{x})'=a^{x} \ln(\log _{a}x)'= \frac {1}{x \ln a}(\arctan x)'=- \frac {1}{1+x^{2}} 基本积分表:ftgxdx=- \ln \cos x+C \int \frac {dx}{ \cos ^{2}x}= \int sec^{2}xdx=tgx+C \int ctgxdx= \ln \sin x+C \int secxdx= \ln \mid secx+tgx \mid+C \int _{ \sin ^{2}x}^{0x}= \int \cos c^{2}xdx=-ctgx+C \int cscxdx= \ln \cos cx-ctgx+C \int secxtgxdx=secx+C \int \frac {dx}{a^{2}+x^{2}}= \frac {1}{a} \arctan \frac {x}{a}+C \int cscxctgxdx=-cscx+C \int _{x^{2}-a^{2}}dx= \frac {1}{2a} \ln \mid x-a \mid+C fa^{x}dx= \frac {a^{x}}{ \ln a}+c fshxdx=chx+C \int \frac {dx}{a^{2}-x^{2}}= \frac {1}{2a} \ln \frac {a+x}{a-x}+C fchxdx=shx+C \int \frac {dx}{ \sqrt {a^{2}-x^{2}}}= \arcsin \frac {x}{a}+C \int \frac {dx}{ \sqrt {x^{2} \pm a^{2}}}= \ln(x+\sqrt {x^{2} \pm a^{2}})+C 1_{n}= \int \limits _{0}^{ \frac { \pi }{2}} \sin ^{n}xdx= \int _{0}^{ \frac { \pi }{2}} \cos ^{n}xdx= \frac {n-1}{n} \int \sqrt {x^{2}+a^{2}}dx= \frac {x}{2} \sqrt {x^{2}+a^{2}}+\frac {a^{2}}{2} \ln(x+\sqrt {x^{2}+a \int \sqrt {x^{2}-a^{2}}dx= \frac