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`f(x)={{:(|x|+1,xlt0),(0,x=0),(|x|-1,xgt0):}={{:(-x+1,xlt0),(0,x=0),(x-1,xgt0):}` <br> `xlt0` then `f(x)= -x+1` is a polynomial function <br> `therefore ` for each `alt0`, lim f(x) exists. <br> `xgt0` then `f(x)=x-1` is a polynomial function. <br> `therefore` For each `a gt0,underset(Xrarr1)"lim"f(x)` exists. <br> at x=0 <br> LHL`=underset(xrarr0^(-))"lim"f(x)` <br> `underset(hrarr0)"lim"f(0-h)` <br> `=underset(hrarr0)"lim"-( 0-h)+1` <br> `=0+1=1` <br> Let `0-h=x` <br> `rArr0-hrarr0` <br> `rArr hrarr0` <br> LHL `=underset(xrarr0^(+))"lim"f(x)` <br> `=underset(hrarr0)"lim"f(0+h)` <br> `=underset(hrarr0)"lim"(0+h)-1=0-1=-1` <br> `because LHLneRHL`. <br> `therefore underset(Xrarr0)"lim"f(x)` does not exist. <br> therefore `underset(xrarra)"lim" f(x)` exists for each `a ne0`. Transcript

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00:00 - 00:59 | student at x = 2 X + 100 x is equals to zero and x minus one by X is greater than zero for what value of k does limit X tends to a Apex exit ok let's find this what I'm going to do c h i am going to change this function that takes less than zero then X is less than zero models is Defined by -6.2 days we did this function is equals to minus 1 + 1 then X is less than zero ok and it is zero when X is equals to zero zero van x = 20 and when X is greater than 0 x x x minus one |

01:00 - 01:59 | when X is greater than zero concept concept is polynomial per polynomial function for polynomial function function limit function limit X tends to ke always exist location to see food I am going to take case one get one when X is less than 0.0 is equal to minus 1 + 1 is a polynomial function |

02:00 - 02:59 | therefore limit exist open I am going to take place to get a then get a then again x minus 1 is a polynomial function Jaipur limit I am going to fine tested at X is equals to zero |

03:00 - 03:59 | X tends to zero minus x minus is less than 0.0 - 10 - + 1 upon ok I am going to find right hand limit ok limit X tends to zero + 40 + greater than zero then X is greater than zero this function is defined 20 plus minus 1 minus one where we can see from both is not equals to artist is not equal to 4 x is equals to zero limit not exist |

04:00 - 04:59 | ok so value of a ok their Limited this is our -0 a belongs to a belongs to our -0 ok thank you |

**Define limit what it represents**

**condition of existence of limit evaluation of right hand left hand limit**

**Relation between the value of a function at a point and the limit at a point**

**Limits : Few Examples**

**The algebra of limits**

**Introduction of all indeterminate forms**

**(i) Direct substitution**

**(ii) Factorisation method (0/0 form)**

**Limits:Example of factorisation method**

**(iii) Rationalisation method (0/0 or ∞/∞ form) :**