00:01
In this question, it is given that limit x tends to infinity x power 45 plus x power 43 plus 2 into e power minus x.
00:19
We need to estimate the limit numerically.
00:23
For that limit x tends to infinity x power 45 plus x power 43.
00:34
Plus 2 divided by e power minus x can be written as e power x applying the limits directly we get infinity by infinity using l -opital rule we get limit extends to infinity 45 x 445 444 plus 43 x 422, differentiating 2, we get 0 divided by e power x which is equal to applying the limits we get infinity by infinity.
01:19
Again using l -opital rule we get limit extends to infinity 45 into 44 x power 43 plus 43 into 42 x power 41 divided by e power x which is equal to applying the limits we get infinity by infinity which we denoted as equation 1 from this we can use a l -apital rule till we get a constant on numerator for that, differentiate equation 1, 43 times we get limit x tends to infinity, 45 into 44 into 43, up to 3 into 2 into 1, divided by e power x, which is equal to limit limit x tends to infinity, 45 into 44 into 43 into 3 into 2 into 1 into 1 by e power x.
03:24
Now, picking out the constants, that is 45 into 44 into dot dot 3 into 2 through into 1.
03:39
X tends to infinity 1 by e power x...
