Math Analysis Homework - Week 14
Math Analysis Homework Week 14 Class 1 T1 <div class="cbox" 2. 讨论下列无穷乘积的敛散性: (2) </div <div class="pbox" 敛散性等价于 $ \prod {n=2}^{\infty} \left(\frac{n^2 1}{n^2 + 1}\right)^p \ (p \i...
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Math Analysis Homework - Week 13
Math Analysis Homework Week 13 Class 1 T1 <div class="cbox" 1. 判断下列级数的敛散性, 绝对收敛还是条件收敛? (2) ; </div <div class="pbox" 递减,莱布尼茨判别法知收敛 $ \sum {n=1}^{\infty} \sin(\pi \sqrt{n^2+1}) \su...
Math Analysis Homework - Week 12
Math Analysis Homework Week 12 Class 1 T1 <div class="cbox" $ p\in (0,4) p\in ( \infty,0]\cup [4,+\infty) f(x) [a, b] \lim {x\to+\infty}f(x)=A, \lim {x\to \infty}f(x)=B a 0 \int {...
Math Analysis Homework - Week 11
Math Analysis Homework Week 11 Class 1 T1 计算曲线围成的面积 <div class='cbox' $ P(1,0) y=\sqrt{x 2} x x y y=\dfrac{1}{2} x \dfrac{1}{2} \iff x=2y+1 r=a(1+\cos\theta) \left(0 \leqslant \th...
Math Analysis Homework - Week 10
Math Analysis Homework Week 10 Class 1 T1 <div class='cbox' $ a<1 a=1 a\ge 1 \vert f(x) \vert <\sqrt 2+1 $ </div
Math Analysis Homework - Week 9
Math Analysis Homework Week 9 Class 1 T1 <div class='cbox' $ f(x 0)\ne 0 f(x 0) 0 (x 0 \delta,x 0+\delta) \forall x\in (x 0 \delta,x 0+\delta),f(x) \dfrac{f(x 0)}2 0 \int x^kf(x)...
Math Analysis Homework - Week 8
Math Analysis Homework Week 8 Class 1 T1 <div class='cbox' $ $ </div
Math Analysis Homework - Week 7
Math Analysis Homework Week 7 Class 1 T1 <div class='cbox' $ a,b 0 4 5 o(x^5) $ </div
Math Analysis Homework - Week 6
Math Analysis Homework Week 6 Class 1 T1 <div class='cbox' analysis the function's convexity and inflection point $ ab=0 a,b\ne 0 a $ </div
Math Analysis Homework - Week 5
Math Analysis Homework Week 5 Class 1 T1 <div class='cbox' $ f(b) f(a) \vert k \vert f'(x 1),f'(x 2) a=0 f(x) 0 (c,d) f(c)=0 f(x) 0,\forall x\in (c,d) g(x)=\ln \vert f(x) \vert \v...
Math Analysis Homework - Week 4
Math Analysis Homework Week 4 Class 1 T1 <div class='cbox' $ $ </div
Math Analysis Homework - Week 3
Math Analysis Homework Week 3 Class 1 T1 <div class='cbox' $ f(0) $ </div
Math Analysis Homework - Week 2
Math Analysis Homework Week 2 Class 4 T1 <div class="cbox" 设 </div <div class='pbox' $ 0 < a 1 < b 1 a {n+1} = \sqrt{a n b n}, b {n+1} = \frac{a n + b n}{2}, n \in \mathbb{N} + \{...
Linea Algebra Homework - Class 1
Linear Algebra Class1 Homework T2 <div class='cbox' Going around a triangle from to to to , what are those three vectors ? What is ? What are their lengths , , and ? The length sq...
Math Analysis Homework - Week 1
Math Analysis Homework Week 1 Class 1 Homework T1 <div class='cbox' </div <div class='pbox' Obviously wrong. $ a n=2^{ n} A 0 \epsilon<A n N a n 0 a n 0 ,\epsilon 1<1,\epsilon 2<A...