00:01
Hello students, here it is given that limit x approaches 1, f of x equal to 6 and the given function is f of x equals to 4 ax cube plus 8 for x less than or equal to 1 and ax plus b for x is greater than 1.
00:28
Here we can use the left side and right side limits.
00:32
If x is less than 1, then the limit x tends to 1 minus that is limit approaches from left f of x equal to limit x tends to 1 minus that is x is less than 1, then the function will be 4 ax cube plus 8.
00:59
Here we can apply the limit therefore it will be 4a plus 8.
01:07
We know that if limit x tends to a plus f of x equal to limit x tends to a minus f of x equal to f of a, then limit x tends to a of x equal to f of a.
01:39
Here we can consider f of a that is limit x tends to 1 minus f of x equals to limit x tends to 1 f of x.
01:57
Here limit x tends to 1 minus f of x is 4a plus 8 and it is given that x tends to 1 f of x is by solving this we will get the value of a that is 4a equal to minus 2, then a will be minus 1 by 2.
02:17
Next we have to consider the limit x tends to 1 plus that is if x is greater than 1, the limit x tends to 1 plus f of x equal to limit x tends to 1 plus f of x.
02:35
Here f of x is ax plus b where the limit approaches 1 from the right.
02:43
So f of x is ax plus b...