Chapter 2

Chapter 2 Limit and continuity ,[object Object],[object Object],[object Object],[object Object],[object Object]

1)Tangent lines and the length of the curve ,[object Object]

[object Object],[object Object]

2)The concept of limit ,[object Object],[object Object],[object Object],[object Object]

Thus, we can conclude that the limit of f(x) when x approaches 2 is 4 and we write ,[object Object],We can see also that when x get closer to 2 from right side, f(x) get closer to 4 3.9999 1.9999 3.999 1.999 3.99 1.99 3.9 1.9 4.0001 2.0001 4.001 2.001 4.01 2.01 4.1 2.1

Since the limits from the two sides are different, we conclude that the limit of g(x) when x approaches 2 doesn’t exist ,[object Object],We can see also that when x get closer to 2 from right side,g(x) decrease very fast toward 10003.9999 1.9999 1003.999 1.999 103.99 1.99 13.9 1.9 -9995.9999 2.0001 -995.999 2.001 -95.99 2.01 -5.9 2.1

[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

3)Computation of the limit ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

4)Continuity of Functions ,[object Object],[object Object],[object Object]

So the function sin(x) is continuous at x=0

So the function f(x) is not continuous at x=3

So the function f(x) is not continuous at x=0

Problem 14 Answer Removable Removable Not removable

[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

[object Object],[object Object],[object Object],[object Object]

[object Object],[object Object],[object Object],[object Object],[object Object]

Limit involving infinity, Asymptotes ,[object Object]

Chapter 2

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Chapter 2