**Analysis** is the study of Functions, using the main tool “**Limit**“.

Limit problems appear in:

1. Continuity

2. Derivative

3. Integral

4. Sequence

**Multi-variable Functions **have different approach of Limit compared to Single-value functions.

Eg. L’Hôpital Rule is **not** applicable to Multi-variable Functions.

**Case 1:** Find the Limit (**L**) of

Solution:

Consider the point P(x,y) on f(x,y)

but when P moves along y=x straight line approaching (0,0),

ie. x->0, y=x->0,

From (1),(2),(3) there are 3 limits {0, 0, 1/2}, hence the Limit **L** does not exist.

**Case 2:**

Find limit L of

**Solution**:

Let y= kx

When x -> ,

f(x,y) independent of k => possible limit of 0

Prove:

Note:

[QED]

**Source:** Prof Zhang ShiZao 章士藻(1940-) “Collected Works of Mathematics Education” 数学教育文集

for Ecole Normale Supérieure in China 高等师范学院

[Video in French ] http://touch.dailymotion.com/video/x89qux