00:01
For this problem, we want to find the limit of x over the square root of x squared minus x as x approaches negative infinity.
00:09
So the first thing i had to do is to rewrite this function by factoring out the variable with the highest exponent.
00:22
So it will be limit as x approaches negative infinity of x over, we have squared of, we factor out x squared inside we get 1 minus 1 over x and then simplifying that we get a limit as x approaches negative infinity of x over square times the square root of 1 minus 1 over x now since our x is approaching negative infinity then our square equals negative x and this should equal to the limit as x approaches negative infinity of x over negative x times the square of one minus one over x.
01:06
Now this cancels out the x and we're left with limit as x approaches negative infinity of negative 1 over the square root of 1 minus 1 over x.
01:19
So evaluating now we get negative 1 over square root of 1 minus 1 over negative infinity and because 1 over and infinity.
01:30
Value goes to 0, then we have here negative of 1 over the square of 1 equal to negative 1.
01:40
So this is the value of our limit.
01:43
Now for the next one, we want to find the limit of the function square root of x squared minus 4 over 9x minus 3 as x approaches infinity.
01:54
So first thing you have to do is to rewrite this by factoring out the variable with high 6.
02:00
Exponent.
02:01
So we do limit as x approaches infinity of the squared of factor out x squared, so times 1 minus 4 over x squared...