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1、若limf(x)=C,x趋于无穷,则有水平渐近线y=C;2、若limf(x)=无穷,x趋于x.,则有垂直渐近线x=x;另外,若limf(x)/x=k不等于0,x趋于无穷,lim(f(x)-kx)=b,x趋于无穷,则有些渐近线y=kx+b。当曲线上一点M。
一、四则运算求极限
1、易错点
①无穷减去无穷不等于0
②1的无穷次方不等于1,要利用等价无穷小或者利用取对数求解
要求渐近线,就是求极限,水平、垂直和斜的,思考要全面.三种渐近线:若limf(x)=C,x趋于无穷,则有水平渐近线y=C;若limf(x)=无穷,x趋于x.,则有垂直渐近线x=x.;若limf(x)/x=k不等于0,x趋于无穷,lim(f(x)-kx)=。
③使用等价无穷小时要注意x是需要趋近于0的
④等价无穷小代换要在乘积时才能替换
2、常见有界函数:三角函数
有界函数乘无穷小量等于0
3、运用夹逼定理求极限
One,four,calculate the limit
1. The error prone point
① Infinity minus infinity is not equal to 0
② The infinite power of 1 is not equal to 1. Use equivalent infinitesimal or take logarithm to solve it ③ When using equivalent infinity,note that x needs to approach 0
3. Use the pinch theorem to find the limit
二、判断函数连续性
1、一般题目会给出分段函数,使函数连续就需要使间断点两侧极限相等。
当x趋于负无穷时,y的极限值为ln2,因此其水平渐近线为y=ln2。3、斜渐近线的求法:求斜渐近线,通常是当x趋于正无穷或负无穷时,求y/x的极限值,此时的值就是a。然后再求x趋于无穷时,(y-ax)的极限值,此时的值。
2、易漏知识点:同阶无穷小、高阶无穷小等概念
Judge the continuity of function
1. The general problem will give a piecewise function. To make the function continuous,you need to make the limits on both sides of the breakpoint equal.
2. Leaky knowledge points: concepts such as infinitesimal of the same order and infinitesimal of higher order
三、判断间断点
1、做题步骤
①分析哪些是间断点(根据定义域判断)
②对相应点求极限
③根据极限情况判断间断点类型
2、易错点:在遇到a^x、e^x,arctanx,arccotx...这些函数时,需要讨论左右极限。对于分段函数也要讨论左右极限。
Judgment of breakpoints
1. Steps for doing the question:
① Analyze which breakpoints are (according to the definition domain)
② Calculate the limit of the corresponding points
四、零点、介值定理
2、例题
Zero point,intermediate value theorem
要求渐近线,就是求极限,水平、垂直和斜的,思考要全面。三种渐近线:若limf(x)=C,x趋于无穷,则有水平渐近线y=C;若limf(x)=无穷,x趋于x。则有垂直渐近线x=x。若limf(x)/x=k不等于0,x趋于无穷,lim(f。
五、判断渐近线
1、水平渐近线:y=a
铅直渐近线:x=b
斜渐近线:
Judge asymptote
1. Horizontal asymptote: y=a
Vertical asymptote: x=b
Oblique asymptote:
(I still hope you can practice more,see different types of questions,and practice your hand!!!)
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