主题：高数 · MIT 18.01
1.Differentiation
in the tangent problem
example 1 is the tangent line of $f(x)=\dfrac{1}{x}$ at point $(x_0,y_0)$
example 2 is $f(x)=x^n$
in the real problem
learn from average rate of change to instantaneous rate
from $\dfrac{\Delta y}{\Delta x}$ to $\dfrac{dy}{dx}$
2.Limits & Continuity
1.How to deal with the tangent problem?
We let the secant line approach the tangent line.
当割线PQ中，点Q趋近于点P时，割线趋近于切线
$\lim_{Q \to P}$ secant line = tangent line
2.How to compute the tangent line?
What we know is the point $P(x_0,y_0)$,and what we need is the slope of the tangent line.
$m = \lim_{\Delta x \to 0} \dfrac{\Delta y}{\Delta x}$
for example:facing the function $f(x)=\dfrac{1}{x}$,the $m$ (slope) is the derivative of f at point $P$
3.The example function I learnt in the class
one is $f(x)=\dfrac{1}{x}$,one is $f(x)=x^n$
4.Limits and Continuity
there are two limits,one is the right-hand limit,another is the left-hand limit.
R:$\lim_{x \to x_0^+}$ It means that $x$ goes to $x_0$ and $x > x_0$
L:$\lim_{x \to x_0^-}$ It means that $x$ goes to $x_0$ and $x < x_0$
the continuity: If $\lim_{x \to x_0} f(x)=f(x_0)$,we say that $f(x)$ is continuous.
three conditions:
one example is the error of GPS,I don't know how the equation is computed.
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