Day 10

Limits of trigonometric functions (no proof for now -only memorise)

The property is derived from squeeze theorem (because substitution produces 0/0) Sq Theorem Video Khan

Results

Lim x =>0    ( sin x)/x  =1

Lim x=>0     (1-cos x)/x  = 0

Lim x=>0    (tan x)/x = 1

TIP:  Squeeze theorem  is a useful tool for solving.However you should develop the skill to identify problems (in limits only) where it can be applied.I noticed that when you are given a function (mainly combined with trigonometric) , where   limits of a part of the function are known,then the problem can be manipulated algebraically (by addition,subn, multpln, divn,exp ) and fitted to suit the application of the theorem and limits derived for the function.The blog will not deal with it as it can be done at school...however remember the above limits.

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We shall be doing problems in derivatives after completing the intro in slides.
Visual Intro to derivatives-slide show