#MathUnusual | Evaluate limit

Hello friends, this is Mahesh Yulekar and you are watching Next Gen Maths. Evaluate limit x tends to 2, 3 power x plus 3 power x minus 1 minus 12 divided by 3 power minus x by 2 minus 3 power 1 minus x. If you want to solve then stop the video otherwise let's start with this. Now 3 power x minus 1 can be written in the form of 3 power x divided by 3. In the denominator 3 power minus x by 2 written in the form of 1 upon 3 power x by 2 minus 3 power 1 minus x written in the form of 3 by 3 power x. Now if we take 3 as the same in the numerator and 3 power x is the same in the denominator then we have 1 by 3, 3 into 3 power x plus 3 power x minus 36. In the denominator we have 1 upon 3 power x into 3 power x by 2 minus 3. Now if we simplify then the denominator of denominator will be the numerator so 3 power x is in the numerator and 3 is in the denominator. 3 plus 1 will be the 4 into 3 power x minus 36 divided by 3 power x by 2 minus 3. Now in the numerator 4 is a common factor so take out from the bracket we have 4 into 3 power x, 3 power x minus 9. If we put 3 power x by 2 equal to t, x approach to 2 so 3 power 2 by 2 equal to 3 so t approach to 3. Then limit t tends to 3, 4 into 3 power x will be the t square so t square minus 9 divided by t minus 3. Now in the numerator t square minus 9 into factorize t plus 3 t minus 3. So from the numerator and denominator t minus 3, 3 minus 3 cancel and we have 4 into t square t plus 3 divided by 3. Now substitute the value of t equal to 3 we have 4 into 3 square 3 plus 3 divided by 3 so 3, 3 cancel and we have 4 into 3 into 6 which is 72. Next chapter.