1. ## Limits

2. Originally Posted by alexandriaruth

Hint: for each problem, multiply by the conjugate over itself, for instance, for the first you would multiply by $\displaystyle \frac {\sqrt{x^2 + 14x - 5} + x}{\sqrt{x^2 + 14x - 5} + x}$. see if you can take it from there

3. i have tried that but i keep just rearranging the function and i never get an answer
14x-5/{(sqrt(x^2)+14x-5)+x}

4. Originally Posted by alexandriaruth
i have tried that but i keep just rearranging the function and i never get an answer
14x-5/{(sqrt(x^2)+14x-5)+x}
factor $\displaystyle x^2$ out of the square root. you get

$\displaystyle \frac {14x - 5}{\sqrt{x^2} \sqrt{1 + \frac {14}x - \frac 5{x^2}} + x} = \frac {14x - 5}{|x| \sqrt{1 + \frac {14}x - \frac 5{x^2}} + x}$

now in this case, since $\displaystyle x \to \infty$, we have $\displaystyle x$ is positive, and hence, $\displaystyle |x| = x$, so we get

$\displaystyle \frac {14x - 5}{x \sqrt{1 + \frac {14}x - \frac 5{x^2}} + x}$

now divide the top and bottom by $\displaystyle x$ and take the limit