00:01
In this question, we have given a function of f -of -x which is the find is x -dose to the power 2 minus 4, whole divided by x minus 2.
00:11
If x is less than 2, x -wet minus vx plus v.
00:21
F2 is laser on the 1 % x is less than x is less than 3.
00:28
And 2x minus a plus b x x is lower equals to 3 and we have to find the value of a and b so that fopets is continuous everywhere so as we know that a function f fx is continuous is continuous.
01:16
Only is left -hand limit at that point same is right -hand limit.
01:32
So here, f is continuous at x equals to 2.
01:45
If limit x tends to minus 2 f f of x the same as limit x tends to 2 plus f of that.
01:59
So from the definition of a function, it implies limit x tends to 2 minus x squared minus 4 divided by x minus 2.
02:12
This is equal to limit x tends to 2 plus x square minus vx plus 3.
02:23
It further implies limit x tends to 2 minus x minus 2 multiplied with x plus 2.
02:35
Here we have factored the value of x squared minus 4, whole divided by x minus 2.
02:43
It is equal to limit x tends to 2 plus x square minus bx plus 3.
02:53
Here x minus 2 is common in both numerative and denominator so we can cancel it out and we are left with limit x tends to 2 minus x plus 2 is equal to limit x tends to 2 plus x square minus b x plus 3 so now if we substitute the limit then we can write it as limit h tends to 0 minus h plus 2 is equal to limit h tends to 0 a 2 plus h whole square minus b 2 plus edge plus 3 here as we approaching to the 2 from the left side so i have subtracted a h from 2 which is tending to 0 and we are here we are approaching to h to 2 from the right hand side so i have added h which is standing to 0 so on simplifying it we get 2 plus 2 equals 2 2 to to the covered 2 multiplied with a minus b multiplied with 2 plus 3 here i have substituted the value of h which implies 4 is is equal to 4a minus 2b plus 3 which implies 4a minus 2b is equal to 1 let us name this equation is equation 1 now f if is continuous at x is equal to 3 if when only if limit x tends to 3 minus f of x is same as limit x tends to 3 plus f of it.
05:05
So it can be written as limit x tends to 3 minus.
05:13
The definition of a function is ax square minus bx plus 3...