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00:00 - 00:59 | the question is if x = 2 x square minus b if Mod X is less than one and one upon Mod x if product is greater than or equal to 1 is differentiable at X = 21 find a and b now we have given function f x = 2 x square minus b if not X is less than one and one upon Mod x if x is greater than or equal to 1 now we know that if Mod X is less than 1 this implies Axis between -1 and 1 and if what does is greater than or equal to 1 this implies X is less than or equal to -1 or access greater than or equal to 1 so hair function is if |

01:00 - 01:59 | x is less than or equal to -1 if -1 less than or less than 1 and if x is greater than or equal to 1 so hair we have the function is if x is less than or equal to -1 then the function is minus one by X because we are taking values of X less than zero so it will be - now if x is between -1 and 1 then it is a square minus b m if it is greater than or equal to 1 then 1 by x and y are given that affects is differentiable at X = 21 so we know the result that if f is differentiable at X = 21 this implies f is continuous at X = |

02:00 - 02:59 | 21 we have limit X tends to 1 minus f x is equals to Limit X tends to 1 + F X is equals to a 4-1 now here if we see extends to 1 - X is equals to F of one so hair for 1 -2 function is x square minus b this implies limit X tends to 1 - x square minus 1 equals to F1 is 1 upon 1 + 1 this implies a into 1 minus b equal to 1 this implies a minus b is equal to 1 JEE question 1 |

03:00 - 03:59 | now we have given that the function is differentiable at X = 21 so this implies left and derivative at X = 21 is equals to right hand derivative at X = 21 now we have limit X tends to 1 minus x minus f of 1 upon x minus 1 is equals to Limit X tends to oneplus effects of of 1 upon x minus 1 which implies limit X tends to 1 minus for the value of x less than 1 the function is x square minus b minus half of one is one upon x minus 1 is equals to Limit gents 21 plus for |

04:00 - 04:59 | the value of x greater than 1 the function is 1 by X + 1 by x minus 1 upon x minus one we get from here that from equation 1 a minus b is equals to 1 implies b is equals to minus one we have limit X tends to 1 minus we have a x square minus A minus 1 minus one upon x minus 1 is equals to Limit X tends to 1 + 1 - X upon X into x minus 1 so we have limit X tends to 1 - x square minus A + 1 minus one upon x minus 1 is equals to Limit X tends to 1 plus minus x |

05:00 - 05:59 | minus one upon X into x minus 1 this implies we have limit X tends to 1ah square minus one and one will be cancel out upon x minus 1 is equals to X - 1 x minus 1 cancel out so we get limit X tends to one plus minus one upon X we have a limit X tends to 1 minus a x square minus one upon x minus 1 is equals to Limit X tends to one plus minus one upon x now we know that x square minus 1 is equals to x minus 1 into X + 1 limit X tends to 1 minus a x - 1 X + 1 upon x minus 1 is equals to |

06:00 - 06:59 | Limit X tends to one plus minus one by X this implies X - 1 x minus 1 cancel out so we get a into 1 + 1 is equals to minus 1 upon 1 which is equals to is equal to minus 1 by 2 now by question 1 we have 20 equals to a -1 this implies b is equals to minus 1 by 2 minus 1 is equal to minus 3 y do we get 20 equals to minus 3 by 2 is equals to minus 1 by 2 and b is equals to minus 3 by 2 and we are done |