考研数学知识库

摘要： 题目 若函数 \(f(x)=\left\{\begin{matrix} \frac{1-\cos\sqrt{x}}{ax}, x > 0 \\ b, x\leqslant 0 \end{matrix}\right.\)，在 \(x=0\) 处连续，则（） ( A ) \(ab = \frac{1}{ 阅读全文

摘要： 题目 判断函数 \(f(x)=ln(x+\sqrt{1+x^{2}})\) 的奇偶性。 解析 本题用到的知识点 \(log_{a}(MN)=log_{a}M+log_{a}N\) 在 MATLAB (下面的代码在 MATLAB 9.1.0.441655 (R2016b) 中测试通过) 中输入如下代码 阅读全文

摘要： 题目 $\lim_{x \to 0}\frac{\sqrt{1+x}+\sqrt{1-x}-2}{x^{2}}=$ 解法一 使用四则运算将原式化简，之后使用等价无穷小替换求出结果。$\lim_{x \to 0}\frac{\sqrt{1+x}+\sqrt{1-x}-2}{x^{2}}=\lim_{x 阅读全文

摘要： 例题：对下面的函数求导$f(x) = \sqrt{1+x} + \sqrt{1-x} - 2$ 错误的求导过程${f}'(x) = {(\sqrt{1 + x})}' + {(\sqrt{1 - x})}' + {2}'={((1 + x)^{\frac{1}{2}})}' + {((1 - x)^ 阅读全文

摘要： 关于等价无穷小的更多内容在这里。 更多高等数学、线性代数、概率统计、考研数学的笔记在这里。 当 $x\rightarrow0$ 时(01) $sin x \backsim x$(02) $tan x \backsim x$(03) $arcsin x \backsim x$(04) $arctan 阅读全文

摘要： One It was many and many a year ago, In a kingdom by the sea, That a maiden there lived whom you May know By the name of ANNABEL LEE; And this maiden 阅读全文

摘要： One I love you, Not only for what you are, But for what I am When I am with you. I love you, Not only for what You have made of yourself, But for what 阅读全文

摘要： One He hugged his son, knowing that he had been a good father. He kissed his wife on the forehead one last time. The old man smiled and closed his eye 阅读全文

摘要： One I hope you see things that startle you. I hope you feel things you never felt before. I hope you meet people with a different point of view. I hop 阅读全文