The importance of micro-element thought

The importance of micro-element thought

@ (Calculus)

On this side of calculus, we often say that micro-elements are the core and an important support concept for understanding calculus. Only the Newton-Leibniz formula will solve the problem, the two-dimensional integral, triple integral or four curve surface area points, not understanding the micro-element.

For example, if you do not have the flexibility to convert the visual angle, the identification of the micro-element, it is difficult topic.

Set F (x) can be directed, f (x, y) =12y∫y−yf (x+t) DT f (x, y) = \FRAC{1}{2Y}\INT_{-Y}^YF (x+t) DT, wherein −∞<x<+∞,y>0-\infty 0. Solve three problems:
1) limy→0+f (x, y) \lim_{y\rightarrow 0^+}f (x, y)

2) Arbitrary y>0 solution Δfδx \frac{\delta F}{\delta x}

3) Ask Limy→0+δfδx \lim_{y\rightarrow 0^+}\frac{\delta F}{\delta x}

Analysis: for 1), is a very direct solution to the limit, the law can be Rockwell.

Limy→0+f (x, y) =limy→0+12y∫y−yf (x+t) dt=limy→0+f (x+y) +f (x−y) 2 \lim_{y\rightarrow 0^+}f (x, y) = \lim_{y\rightarrow 0^+} \ FRAC{1}{2Y}\INT_{-Y}^YF (x+t) dt \ \ = \lim_{y\rightarrow 0^+} \frac{f (X+y) +f (x-y)}{2}

Note that this is the variable upper bound + variable lower bound integral, so the derivative is multiplied by the upper and lower bound to Y. By the right, here y is the micro element. The meaning of the yuan is variable, but it tends to be 0. The variables that tend to be 0 in mathematics are interesting and integrable.

Here, the denominator is already a constant, no longer the denominator tends to 0 limit, then back to focus on the molecule. According to test instructions,