Question

My teachers key says that it us -2. I was never taught how to evaluate limits that go to infinity or negative infinity so I need to be taught how to solve them.

Answer 1

The given limit is:

`\lim_(x\to-\infty)(√(4x^2+5))/(x-3)`

Divide by the numerator and denominator by x

Upon simplifying this gives:

Taking the limit gives:

`\begin{gathered} \frac{\sqrt{4+(5)/(-\infty)}}{1-(3)/(-\infty)} \\ (√(4+0))/(1-0) \\ =(\pm2)/(1) \\ =\pm2 \end{gathered}`