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00:00 - 00:59 | we have the question if update X is equals to jio packs into x minus 8 function where jio ke is not ji is ji function is continuous at X is equals to a then we have to check whether out of the given a b c and d which option is correct regarding the function f with respect to the latest write a function that we have we have at the check is equals to jio X into x minus A this is given to us have given that jio packs is continuous at X is equals to |

01:00 - 01:59 | now by this statement that jio packs is continuous at X is equals to a mean by the limit that left limit is equals to right hand limit and which is equals to a function which is what we mean by appointing a function that is left hand limit and writing is equal and it is equal to the value of the function at that point the value of left it means that limit X tends to a negative function ji of these are the points of X which are to the limit of text into a in these are the points which are in the right of x is equal to |

02:00 - 02:59 | this will be equal to jio latest understand this with a graph we mean that if D is a point to point a then they are saying jio fixed is a function continuous at x = if a function is continuous at a point P name that graphically that if we make a small to small labour this neighborhood around this a point then if we move towards this a point in the value of x from the left side of the left side of a then we will be taking |

03:00 - 03:59 | when use approximately equal to the value of g of it and as we move from right side of a word that this value will be taking the value of symmetry and exactly equal to jio also left hand limit so this is what we mean by continuous function so it can also be written as in the term at some distance at and this will be written as a minus H for the left inside because we know in the left is less than a year and will be a minus replaced with a minor such as limit X tends |

04:00 - 04:59 | now for right inside we know X are greater than right inside Alexa greater than a so this this can be say that a + HS equals to X limit X tends to zero + H is equal to what what we have concluded the conclusion now it is also question that jio is not equal to zero so that means if jio SIM is not equal to zero and G of UNO is equal to from which is a + b |

05:00 - 05:59 | is also not equal to see and by the properties of limit we can say that if a limit at a point is not zero then that will not equals to zero that is this function GF am I a + H with not equal to zero by the property of limit this window so this is the latest consider the function that we have again this is a function of the shell as we 2 which is |

06:00 - 06:59 | now since we were considered about the value of the function in the neighbourhood of a is a is then in the neighbourhood of a the values here and left hand limit are the values less than a and these are the values in the right of way so what are the values that are to the left of a we can say these values are less than it and for the values that are the right greater than X 35 this value and all X in the right hand side satisfied is valued at is actually the distance between exist |

07:00 - 07:59 | in the left hand side then this distance is the distance between this X and Y we are saying that it is at so this distance is always positive positive let is considered the value of x in the left hand side of a writer for neighborhood lesson a we can put x is equals to minus in f dash so function at the left inside |

08:00 - 08:59 | this we are talking about the value of a dash in the left neighbourhood first letter will be jio a minus 6 and this can a cancer at CEO at into this is the distance it can never squared is so this means is positive Northeast hsv igg is positive then the sign of f dash am - h directly depends on the sign of a minus x only that jio a minus x is not equal to zero |

09:00 - 09:59 | so that means either rioplay - h is greater than zero on lesson the graph graphs is this point then corresponding to this point distance from point P of a in the now these are the points that are a minus at corresponding to each a minus x we will be getting some point in the neighborhood and corresponding to the point that jio if we have given that jiofi is also not equal to zero is equal to zero then |

10:00 - 10:59 | we are considering the keys similarly we could talk about the case is less than zero then the never will be here so these are the same cases we can consider it here considered here then clearly if A is greater than zero then in the neighbour jio into the values of R positive in this particular neighborhood so we can say in a particular day Jiyo Jiyo A is greater than 0 in a neighborhood then that neighborhood just a minus x is greater than zero |

11:00 - 11:59 | and gift of a minus is greater than zero then we can say that this is also provided in this is also produces zero this implies after dash a minus is also greater than zero also be considered the value of jio that means your free is less than zero and if it is less than zero we can make a neighborhood around it never worked around jio a value corresponding to a minus b and a plus will be 10 in this particular neighborhood because g of a is less than zero so we can say that if g is less than in that neighborhood - hba0 |

12:00 - 12:59 | and utilizes a minus is less than zero so we can conclude from here if a is zero then update a minus that means function is increasing function because its first derivative is greater than zero for all values that are satisfied this a minor scratch that is all values that lies in this interview less than zero then after she - which is less than zero for this means is decreasing for in the am so what we can do with your conclusions |

13:00 - 13:59 | that if x is increasing is left neighborhood just talking about left their neighborhood and if x is in decreasing is less than zero from here this is also in the left neighborhood a now this conclusion that we have shown for left nevertheless they can also be shown for the write neighborhood of the difference will be just a then be done as a plus and then left dash A+ A+ H2H square |

14:00 - 14:59 | + 3 equal or greater than zero if then off + h20 just been employed as a + H is greater than and then we can say is increasing for the right neighborhood of A and B if b is the less than zero then a + H will be nice A+ h will be less than zero and function is decreasing for the right neighborhood of a that either the left or right neighborhood increasing |

15:00 - 15:59 | is greater than zero function is decreasing when is less than zero w both the neighborhood so the correct answer for this question is as increasing in the neighbourhood of a sphere is greater than zero this neighborhood could be either or writing table also the question is this option number de because life is decreasing in the neighbourhood of a listen to the correct a and b |