Question

To find the limit as x approaches infinity for the given expression: lim x→[infinity]−6x²+25x²+7x−9

Answer 1

To find the limit as x approaches infinity for the expression, we can use the fact that the limit of a sum is equal to the sum of the limits. The limit as x approaches infinity for the expression -6x²+25x²+7x−9 is infinity.

Step-by-step explanation:

To find the limit as x approaches infinity for the expression lim x→[infinity]−6x²+25x²+7x−9, we can use the fact that the limit of a sum is equal to the sum of the limits. We can also ignore terms that become insignificant as x approaches infinity. Here's the step-by-step solution:

1. Combine like terms: -6x²+25x² = 19x²
2. Write the expression as a sum: 19x²+7x−9
3. Take the limit of each term separately:
   • lim x→[infinity] 19x² = infinity
   • lim x→[infinity] 7x = infinity
   • lim x→[infinity] -9 = -9
4. Combine the limits of each term: infinity + infinity - 9 = infinity

Therefore, the limit as x approaches infinity for the expression -6x²+25x²+7x−9 is infinity.