Question

Find the limit
lim _{x=[infinity]} √{x²+14 * x}- √{x²+3 * x}

Answer 1

To find the limit lim √{x²+14 * x}- √{x²+3 * x} as x approaches infinity, we can simplify and apply some algebraic operations. The final result of the limit is 11.

Step-by-step explanation:

To find the limit lim √{x²+14 * x}- √{x²+3 * x} as x approaches infinity, we can simplify and apply some algebraic operations.

First, we rationalize the numerator by multiplying it by the conjugate, which simplifies to (x² + 14 * x) - (x² + 3 * x).Next, we combine like terms in the numerator to get 11 * x.Finally, we divide both the numerator and denominator by x and take the limit as x approaches infinity. This gives us a final result of 11.