Day 9

Do exercise 1.8 from problem book (given below) after the Khan Video in Day 8

Rate of Change Graphs

Day8

.Horizontal asymptotesVideo

This the application of limits(x approaching +ve or -ve infinity) to find horizontal asymptodes-

No other logical or algebraic method exists.

Vertical asymptotes are very easy to find (x value that makes denominator=0)

Find the Limits- (most problems can be done -using the mental short cut trick)

Answers

Video Vertical asymptotes
Limits -infinity related Khan Videos to do

Day 7

Transformation of graphs google slides by TSK Slide editable
For the next exercise you should learn to use the calculator.Calculator based questions are there in AP Calculus,Its allowed for 45 mts or so...but only some problems will need it.

Day 6

Knowledge accumulation for future use:

Library of Functions Video - a good video on basics of function graphing(-missing exponential and logarithmic function graphs)Useful for SAT, algebra,calculus(integral)

Understand the standard term for the type of function (lke identity,quadratic, cubic,reciprocal etc)

{Video on Library of Functions}

Day 5

*After completing trigonometry unit circle (downloadded sheet) by filling it and removing errors if you found any.Check why you made the errors.(Remember  sine is I and so cosine is _ (my hand signal) and relate their signs to quadrants .

 +

*Practice range  of square root functions and log functions

Limits at infinity  (x approaching infinity)

Tip:  In  rational expression only the highest power maaters for the rsult at infinity in numerator and denominator.See iff you can do the limits mentally using that idea as a short cut.after watching the videos.

Limits at infinity video1 (with graph);Limits at Infinty Video 2  ;  Limits at infinity video(square root example) Limits at infinity soving tricks Video  Asymptodes and limits

*Down load exercise on limits at infinity from P.Cal and check answers with the solutions

*Do the connected assignment (no answers)
Recollect

What can you recollect and say about (0-0),(0/0),0+0),(-0-0)?What can you say if you replace 0 by infinity in the question?How do you overcome the problem of powers of 'x' when x approaches + or - infinity.?Scribble you answer and keep it ready for a chat.

Exercise quick review of methods learnt.

Day 4

The unit circle for trigonometric ratios 
Notice that there are 3 important angles between π and π/2.They are 30 deg(π/6) , and 60 deg (π/3)45 deg(π/4).The others can be derived by using their location in the quadrant with signs .A litle practice s sufficient .These ratios will appear throughout the college courses in physics and maths and engineering.
Memorising TIP:(Just think why cosines are always negative left of y-axis.Also why sine are negative below the x-axis.)
The easiest ratios are for 45 deg(π/4) ; sin 45=cos 45=1/√2 and tan 45=1
Sin 60=√3 /2 =Cos 30    and   Cos 60=1/2 =Sin 30

Print the both image by selecting and give a print command to printer and fill the blanks from memory.

Limits Day3

Answers to Exercises in Day 2.

One sided Limits; Example study  Video Extension Video

Limits of trigonometric functions:
1.Review of trignometric ratios and remebering them: Video

Limits Day 2

In the earlier videos and exercises you saw how to find the limits from a graph(plotted readily) with identified undefined values or a different defined value.It was easy to see the approach from below and above a value (say 'a') and declare if the limits were same  if so if it was also the same as f(a).
of the other methods when a graph is not given but a expression (formula of the graph ) is given then  you have to find the limits by algebra...

Video 4.Limits by substitution

Video 5 Limits by factorisation

video 6 Limits by conjugate

Find limits (substitution or by factorisation)
Tip:At times you will find the denominator and the numerator both become "0" on substitution,then you should try factorization. If  by substituting ,for example x=a, results in 0/0,then you know by reminder theorem in algebra,that '(x-a)' must be a factor in numerator and denominator.Using this (x-a) as a factor,you can get the other factors of the Numerator and Denominator.

Day1

A very useful site for Mathematics all topics
Intro to Limits

The topic of limits in calculus is important only upto the stage of start of differential calculus.Thereafter it looses its utility in most of calculus.It appears briefly in definite integrals and thereafter in Series(AP BC) .But the concept is the most important stepping stone for entry into the subject of calculus.The concept of limit is the one that enable one to examine microscopically at the behavior  of functions, which otherwise seem to be just expressions .It enables you to examine as if you are looking at an  atomic particle inside a molecule just by applying simple mathematical tools (learnt in 9th grade level algebra-geometry-trigonometry)

First Blast

Study the videos below-pause and replay if you did not understand some thing-and try to answer the following questions.

You will notice that the video discusses about a function f(x) or may be g(x), and adresses a problem that arises when"x"=some value...

Explain the reason for "the gap".

How does the limt concept overcomes the 'gap problem'?

Limits Intro

First Lessons

Right through the limits chapter and its problems,one fact that can be easily overlooked and make you stumble is that limit is not the same as substituting for 'x' in f(x).....though in some situations  you can find it by substitution. Later you will learn the truth about it and to be watchful.Its for this reason the videos talk about approaching a value and not substituting the value.

Below is Simple intro using a st line function - graph.(DON'Tgo to other videos on the sides-they will come later and will confuse you now)

Video1 limits

You should pay attention to the symbolic way of expressing limit(from left hand side and right hand side)-they can easily confuse you when solving a problem and potential error causing symbols.Try to understand the difference between the approaching a limit value from a negative side and the positive side (I say in my mind -as from below the value and above the value...that reduces  errors).Later you will do lots of problems involving the side of approach.

video 2.Limits in graphs-left hand and right hand limits

Clear all doubts before watching next viseo.Keep a paper pencil for any scratch work.

video 3. Exercises-Limits from graph

Study the problem below and check answers.

Exercise

1. Below is the graph of .  For each of the given points determine the value of , , , and .  If any of the quantities do not exist clearly explain why.

(a)                       (b)                       (c)                       (d)