00:01
For this problem, we want to take the limit as x approaches 2 of negative x squared plus 5x minus 2.
00:08
So first, we want to apply the sum and difference rules.
00:13
So this becomes the limit as x approaches 2 of negative x squared, plus the limit as x approaches 2 of 5x, minus the limit as x approaches 2 of 2, provided that all of those limits exist separately.
00:34
Then for the first term, we want to apply the constant multiple rule to move the negative outside of the limit, and then we can apply the power rule to move the limit inside the square.
00:47
So we would have negative limit as x approaches 2 of x, quantity, d squared, so now the square is on the outside of the limit.
01:00
Then on the next term, we can use the constant multiple rule to move the five outside of the limit.
01:06
So we have five times the limit as x approaches 2 of x, and then minus the limit as x approaches 2 of 2.
01:15
Again, this is provided that all of these limits exist.
01:19
But we know that the limit of x as x approaches 2 would be 2, because the limit of the constant function is equal to the value that the variable is approaching...