Here is the calculus question on my kids HW.
$$\lim_{x\to -\infty} 7x + \sqrt{49x^2 - x}$$
How would I approach this problem. The solution gets to an answer of $\frac{1}{14}$ but when I graph it out I see that the curve approaches $-\infty$ as x goes to $-\infty$.
How would I get started with this problem? Do start by multiplying the top and bottom by $1/\sqrt{x^2}$ ?
Thanks!
Hint
Method 1 : Multiply your expression by $\frac{7x-\sqrt{49x^2-x}}{7x-\sqrt{49x^2-x}}$.
Method 2 : If $x<0$, $$7x+\sqrt{49x^2-x}=x\left(7- \sqrt{49-\frac{1}{x}}\right),$$ and use the fact that $$\sqrt{49-\frac{1}{x}}=7-\frac{1}{14}\cdot \frac{1}{x}+o\left(\frac{1}{x}\right),\quad \text{whenever }x\to -\infty .$$