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Introduction to Limits:

What is Limits? Before we define what Limits is; itvery important for us to understand basic concept ofLimits, its usage in day to day life. Lets look at anexample: where Limits can be used in day to day life. Continu


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Imagine JOHN and MARK, going to school early morning. JOHN comand

MARK coming from RIGHT. They both arrive at school. They the scboundary. Means they can not go beyond school. So the School is

JOHN

School

C


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So Limits Exits when Both JOHN and MARK Arrive at School. Dont

their Timing.

JOHN

School

C


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Lets look at another example;An aeroplane flying on below RED line, you want to find itsspeeds at point A.

Formula for drawing the red lineis as follow, + 3 Now you wantto find its speed at point say A =4. So you just replace it where

ever you seeIn this case it will be: 4+43 = 4 +

64 = 68


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+ 3 A = 4. So you just replace it

where ever you see . =4+43 = 4+ 64 = 68

Question:Does this graph havelimit?

Continu


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Now let look at last example ofLIMITS.

Imagine you drop a stone into a

bowl from Left, you cancalculate its speed at pointA.

Questionwhat would you do todetermine the speed of stone atpoint A?

L R


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Answer: Turn the bowl graph Upside down.

A

L R


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Earlier we said Limits exist IF AND ONLY IF Function (Graph) iscontinuous.

So what do we mean by continuous?

Lets go back to first example. JOHN and MARK

Continue


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If draw this Line as a graph, it would look like this;

JOHN

School


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Imagine you have hole in to the line, A & B. whaif JOHN and Mark try to go? Yes! They will fall ovmight hurt them self.

John Mark A

B

John Mark

Schoo


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How about this graph? Is it Continuous ordiscontinuous?

Continuous

Continu


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Definition of Limits according to Literature

f (x) = x

2

if you want to find value when the graph if f(x) = x

2

and x = 2, you just replace x with 2.22 = 4

8642

2


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To write this in mathematical formula it follows;

limf(x)= x2

X2It means Limit of our function x2.What is the value when x is replace

by 2 Contin


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limf(x)= x2

X2lim = Limits

f(x) = function to draw line, curve, could be any kindof graph.

=


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Now lets recap;

Mathematical Limits is a Graph or a Curve or a Function.Arrive at a point for Left and Right on that function.


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2. Limit exist IF AND ONLY IF the graph is CONTINOUS.

3. CONTINOUS function is a smooth graph which has no,jump in the graph, has no gap in the graph.


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4. DISCONTINOUS graph is graph where it has break ingraph, wihch is not smooth. Below graph shows 1,-1 Yvalues hence it is not CONTINOUS.REMEMBER a FUNCTION = a GRAPH, means exactlysamething.


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5. Limits According to

Books;

lim f(x) = x2 + x3

x -->2


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lim f(x) = x2 + x3

x -->2

lim = called Limitsf(x) = F of x.x2 + x3 = function to draw graph

x--> 2 = x goes to 2, or xa roches to 2


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TestWhat is Limits? (Check boxes)

a. DISCONTINOUSb. Arriving at a point from Left and Rightc. Continuous Function

d. + 3

2. What is Continuous Graph? (Check boxes)a. a Graphb. Smooth Graphc. Graph with no Jump or Break

d. X 23. Limit Exist IF AND ONLY IF: (radio buttons)

a. Graph has a curveb. The graph is Discontinuous

c. The function is continuousd. The has a point.


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What is function f(x)? (radio buttons)A graphContinuous

LimitsYlim stands for? (radio buttons)limitlittlelimitationslimitarylimitedlimiterOrganise this. (Drag and Drop )

Lim, =, x2, + 3,

f(x)

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7. What f(x) stands for?a. Function of x-mas

b. Function of xc. f of x

8. What is the correct result of f(x) = x+x+3. lim3?a. 3b.3+3c.9d.6e.3*3

9.


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