[AP_Calculus_20150516LIM] Large abyss with no Limit?

Question

Introduction

     This looks like a scary limit to calculate.  Indeed, it is quite tricky, as  x  goes towards negative infinity and there is a square root.  However, we can often work out the correct answer informally first.

Informal Solution (intuitive approach)

Formal Solution

Final Remark

     Having the informal solution (which can be worked out on rough paper or even mentally) gives us an idea of the answer.  We can counter-check our formal solution with the informal solution for confirmation.

Suitable Levels

* Advanced Placement (AP) Calculus AB & BC

* University / college level calculus

* other syllabuses that involve limits