Day 7: Double Conjugate Limit Problem

Find the limit:





Solution: Limits with square roots in the top and bottom are daunting. They require a bit of work as well. Had there been only one square root, the task would be to multiply by the conjugate on the top and bottom. The task at hand is not much different, it requires multiply the top and bottom by both conjugates as follows:





Notice that the operation applied above does not change anything because the top and bottom was multiplied by the same thing, hence, we multiplied the limit by 1. However, the limit simplifies nicely from here:





And now these problems are cake!


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